Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ Question 21: Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s sin xa are fixed non-zero constants and m and n are integers): cos x Solution 21: sin xa Let f(x) = cos x By quotient rule, d d cos x sin x a sin x a cos x ' dx f x dx 2 cos x d cos x sin x a sin x a sin x f ' x dx ... i 2 cos x Let g(x)=sin (x + a). Accordingly, g(x + h) = sin (x + h + a) By first principle, g( x h) g x g' x lim h0 h 1 lim sin x h a sin x a h0 h 1 x h a x a x h a x a lim 2cos sin h0 h 2 2 lim 1 2cos 2x 2a h sin h h0 h h 2 h sin 2x 2a h 2 lim cos h0 h h 2 sin h 2x 2a h 2 h limcos .lim As h 0 0 h0 h h 0 h 2 2 2 2x 2a sinh cos 1 lim 1 2 h0 h cos x a ... ii From (i) and (ii), we obtain Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ sin sin cos x.cos x a x x a f ' x 2 cos x cos x a x 2 cos x cos a 2 cos x Question 22: Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): x 4 (5 sin x - 3 cos x) Solution 22: 4 Let f ( x) x (5sin x 3cos x) By product rule, 4 d d 4 f '( x) x (5sin x 3cos x) (5sin x 3cos x) x dx dx d d d x 5 sin x 3 cos x (5sin x 3cos x) x dx dx dx 4 3 x 5cos x 3sin x (5sin x 3cos x) 4x 3 x 5xcos x 3xsin x 20sin x 12cos x 4 4 Question 23: Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (x 2 + 1) cos x Solution 23: Let f(x) = x 2 1 cos x By product rule, 2 d d 2 f ' x x 1 cos x cos x x 1 dx dx 2 x 1 sin x cos x 2x 2 x sin x sin x 2xcos x Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

- Page 1 and 2:
Class XI Chapter 1 - Sets Maths ___

- Page 3 and 4:
Class XI Chapter 1 - Sets Maths ___

- Page 5 and 6:
Class XI Chapter 1 - Sets Maths ___

- Page 7 and 8:
Class XI Chapter 1 - Sets Maths ___

- Page 9 and 10:
Class XI Chapter 1 - Sets Maths ___

- Page 11 and 12:
Class XI Chapter 1 - Sets Maths ___

- Page 13 and 14:
Class XI Chapter 1 - Sets Maths ___

- Page 15 and 16:
Class XI Chapter 1 - Sets Maths ___

- Page 17 and 18:
Class XI Chapter 1 - Sets Maths ___

- Page 19 and 20:
Class XI Chapter 1 - Sets Maths ___

- Page 21 and 22:
Class XI Chapter 1 - Sets Maths ___

- Page 23 and 24:
Class XI Chapter 1 - Sets Maths ___

- Page 25 and 26:
Class XI Chapter 1 - Sets Maths ___

- Page 27 and 28:
Class XI Chapter 1 - Sets Maths ___

- Page 29 and 30:
Class XI Chapter 1 - Sets Maths ___

- Page 31 and 32:
Class XI Chapter 1 - Sets Maths ___

- Page 33 and 34:
Class XI Chapter 1 - Sets Maths ___

- Page 35 and 36:
Class XI Chapter 1 - Sets Maths ___

- Page 37 and 38:
Class XI Chapter 1 - Sets Maths ___

- Page 39 and 40:
Class XI Chapter 1 - Sets Maths ___

- Page 41 and 42:
Class XI Chapter 1 - Sets Maths ___

- Page 43 and 44:
Class XI Chapter 2 - Relations and

- Page 45 and 46:
Class XI Chapter 2 - Relations and

- Page 47 and 48:
Class XI Chapter 2 - Relations and

- Page 49 and 50:
Class XI Chapter 2 - Relations and

- Page 51 and 52:
Class XI Chapter 2 - Relations and

- Page 53 and 54:
Class XI Chapter 2 - Relations and

- Page 55 and 56:
Class XI Chapter 2 - Relations and

- Page 57 and 58:
Class XI Chapter 2 - Relations and

- Page 59 and 60:
Class XI Chapter 2 - Relations and

- Page 61 and 62:
Class XI Chapter 3 - Trigonometric

- Page 63 and 64:
Class XI Chapter 3 - Trigonometric

- Page 65 and 66:
Class XI Chapter 3 - Trigonometric

- Page 67 and 68:
Class XI Chapter 3 - Trigonometric

- Page 69 and 70:
Class XI Chapter 3 - Trigonometric

- Page 71 and 72:
Class XI Chapter 3 - Trigonometric

- Page 73 and 74:
Class XI Chapter 3 - Trigonometric

- Page 75 and 76:
Class XI Chapter 3 - Trigonometric

- Page 77 and 78:
Class XI Chapter 3 - Trigonometric

- Page 79 and 80:
Class XI Chapter 3 - Trigonometric

- Page 81 and 82:
Class XI Chapter 3 - Trigonometric

- Page 83 and 84:
Class XI Chapter 3 - Trigonometric

- Page 85 and 86:
Class XI Chapter 3 - Trigonometric

- Page 87 and 88:
Class XI Chapter 3 - Trigonometric

- Page 89 and 90:
Class XI Chapter 3 - Trigonometric

- Page 91 and 92:
Class XI Chapter 3 - Trigonometric

- Page 93 and 94:
Class XI Chapter 3 - Trigonometric

- Page 95 and 96:
Class XI Chapter 3 - Trigonometric

- Page 97 and 98:
Class XI Chapter 3 - Trigonometric

- Page 99 and 100:
Class XI Chapter 4 - Principle of M

- Page 101 and 102:
Class XI Chapter 4 - Principle of M

- Page 103 and 104:
Class XI Chapter 4 - Principle of M

- Page 105 and 106:
Class XI Chapter 4 - Principle of M

- Page 107 and 108:
Class XI Chapter 4 - Principle of M

- Page 109 and 110:
Class XI Chapter 4 - Principle of M

- Page 111 and 112:
Class XI Chapter 4 - Principle of M

- Page 113 and 114:
Class XI Chapter 4 - Principle of M

- Page 115 and 116:
Class XI Chapter 4 - Principle of M

- Page 117 and 118:
Class XI Chapter 4 - Principle of M

- Page 119 and 120:
Class XI Chapter 4 - Principle of M

- Page 121 and 122:
Class XI Chapter 4 - Principle of M

- Page 123 and 124:
Class XI Chapter 4 - Principle of M

- Page 125 and 126:
Class XI Chapter 5 - Complex Number

- Page 127 and 128:
Class XI Chapter 5 - Complex Number

- Page 129 and 130:
Class XI Chapter 5 - Complex Number

- Page 131 and 132:
Class XI Chapter 5 - Complex Number

- Page 133 and 134:
Class XI Chapter 5 - Complex Number

- Page 135 and 136:
Class XI Chapter 5 - Complex Number

- Page 137 and 138:
Class XI Chapter 5 - Complex Number

- Page 139 and 140:
Class XI Chapter 5 - Complex Number

- Page 141 and 142:
Class XI Chapter 5 - Complex Number

- Page 143 and 144:
Class XI Chapter 5 - Complex Number

- Page 145 and 146:
Class XI Chapter 5 - Complex Number

- Page 147 and 148:
Class XI Chapter 5 - Complex Number

- Page 149 and 150:
Class XI Chapter 5 - Complex Number

- Page 151 and 152:
Class XI Chapter 5 - Complex Number

- Page 153 and 154:
Class XI Chapter 5 - Complex Number

- Page 155 and 156:
Class XI Chapter 6 - Linear Inequal

- Page 157 and 158:
Class XI Chapter 6 - Linear Inequal

- Page 159 and 160:
Class XI Chapter 6 - Linear Inequal

- Page 161 and 162:
Class XI Chapter 6 - Linear Inequal

- Page 163 and 164:
Class XI Chapter 6 - Linear Inequal

- Page 165 and 166:
Class XI Chapter 6 - Linear Inequal

- Page 167 and 168:
Class XI Chapter 6 - Linear Inequal

- Page 169 and 170:
Class XI Chapter 6 - Linear Inequal

- Page 171 and 172:
Class XI Chapter 6 - Linear Inequal

- Page 173 and 174:
Class XI Chapter 6 - Linear Inequal

- Page 175 and 176:
Class XI Chapter 6 - Linear Inequal

- Page 177 and 178:
Class XI Chapter 6 - Linear Inequal

- Page 179 and 180:
Class XI Chapter 6 - Linear Inequal

- Page 181 and 182:
Class XI Chapter 6 - Linear Inequal

- Page 183 and 184:
Class XI Chapter 6 - Linear Inequal

- Page 185 and 186:
Class XI Chapter 6 - Linear Inequal

- Page 187 and 188:
Class XI Chapter 6 - Linear Inequal

- Page 189 and 190:
Class XI Chapter 6 - Linear Inequal

- Page 191 and 192:
Class XI Chapter 6 - Linear Inequal

- Page 193 and 194:
Class XI Chapter 6 - Linear Inequal

- Page 195 and 196:
Class XI Chapter 6 - Linear Inequal

- Page 197 and 198:
Class XI Chapter 7 - Permutation an

- Page 199 and 200:
Class XI Chapter 7 - Permutation an

- Page 201 and 202:
Class XI Chapter 7 - Permutation an

- Page 203 and 204:
Class XI Chapter 7 - Permutation an

- Page 205 and 206:
Class XI Chapter 7 - Permutation an

- Page 207 and 208:
Class XI Chapter 7 - Permutation an

- Page 209 and 210:
Class XI Chapter 7 - Permutation an

- Page 211 and 212:
Class XI Chapter 7 - Permutation an

- Page 213 and 214:
Class XI Chapter 7 - Permutation an

- Page 215 and 216:
Class XI Chapter 7 - Permutation an

- Page 217 and 218:
Class XI Chapter 7 - Permutation an

- Page 219 and 220:
Class XI Chapter 8 - Binomial Theor

- Page 221 and 222:
Class XI Chapter 8 - Binomial Theor

- Page 223 and 224:
Class XI Chapter 8 - Binomial Theor

- Page 225 and 226:
Class XI Chapter 8 - Binomial Theor

- Page 227 and 228:
Class XI Chapter 8 - Binomial Theor

- Page 229 and 230:
Class XI Chapter 8 - Binomial Theor

- Page 231 and 232:
Class XI Chapter 8 - Binomial Theor

- Page 233 and 234:
Class XI Chapter 8 - Binomial Theor

- Page 235 and 236:
Class XI Chapter 8 - Binomial Theor

- Page 237 and 238:
Class XI Chapter 8 - Binomial Theor

- Page 239 and 240:
Class XI Chapter 8 - Binomial Theor

- Page 241 and 242:
Class XI Chapter 9 - Sequences and

- Page 243 and 244:
Class XI Chapter 9 - Sequences and

- Page 245 and 246:
Class XI Chapter 9 - Sequences and

- Page 247 and 248:
Class XI Chapter 9 - Sequences and

- Page 249 and 250:
Class XI Chapter 9 - Sequences and

- Page 251 and 252:
Class XI Chapter 9 - Sequences and

- Page 253 and 254:
Class XI Chapter 9 - Sequences and

- Page 255 and 256:
Class XI Chapter 9 - Sequences and

- Page 257 and 258:
Class XI Chapter 9 - Sequences and

- Page 259 and 260:
Class XI Chapter 9 - Sequences and

- Page 261 and 262:
Class XI Chapter 9 - Sequences and

- Page 263 and 264:
Class XI Chapter 9 - Sequences and

- Page 265 and 266:
Class XI Chapter 9 - Sequences and

- Page 267 and 268:
Class XI Chapter 9 - Sequences and

- Page 269 and 270:
Class XI Chapter 9 - Sequences and

- Page 271 and 272:
Class XI Chapter 9 - Sequences and

- Page 273 and 274:
Class XI Chapter 9 - Sequences and

- Page 275 and 276:
Class XI Chapter 9 - Sequences and

- Page 277 and 278:
Class XI Chapter 9 - Sequences and

- Page 279 and 280:
Class XI Chapter 9 - Sequences and

- Page 281 and 282:
Class XI Chapter 9 - Sequences and

- Page 283 and 284:
Class XI Chapter 9 - Sequences and

- Page 285 and 286:
Class XI Chapter 9 - Sequences and

- Page 287 and 288:
Class XI Chapter 9 - Sequences and

- Page 289 and 290:
Class XI Chapter 9 - Sequences and

- Page 291 and 292:
Class XI Chapter 9 - Sequences and

- Page 293 and 294:
Class XI Chapter 9 - Sequences and

- Page 295 and 296:
Class XI Chapter 9 - Sequences and

- Page 297 and 298:
Class XI Chapter 9 - Sequences and

- Page 299 and 300:
Class XI Chapter 9 - Sequences and

- Page 301 and 302:
Class XI Chapter 9 - Sequences and

- Page 303 and 304:
Class XI Chapter 9 - Sequences and

- Page 305 and 306:
Class XI Chapter 9 - Sequences and

- Page 307 and 308:
Class XI Chapter 9 - Sequences and

- Page 309 and 310:
Class XI Chapter 9 - Sequences and

- Page 311 and 312:
Class XI Chapter 9 - Sequences and

- Page 313 and 314:
Class XI Chapter 10 - Straight Line

- Page 315 and 316:
Class XI Chapter 10 - Straight Line

- Page 317 and 318:
Class XI Chapter 10 - Straight Line

- Page 319 and 320:
Class XI Chapter 10 - Straight Line

- Page 321 and 322:
Class XI Chapter 10 - Straight Line

- Page 323 and 324:
Class XI Chapter 10 - Straight Line

- Page 325 and 326:
Class XI Chapter 10 - Straight Line

- Page 327 and 328:
Class XI Chapter 10 - Straight Line

- Page 329 and 330:
Class XI Chapter 10 - Straight Line

- Page 331 and 332:
Class XI Chapter 10 - Straight Line

- Page 333 and 334:
Class XI Chapter 10 - Straight Line

- Page 335 and 336:
Class XI Chapter 10 - Straight Line

- Page 337 and 338:
Class XI Chapter 10 - Straight Line

- Page 339 and 340:
Class XI Chapter 10 - Straight Line

- Page 341 and 342:
Class XI Chapter 10 - Straight Line

- Page 343 and 344:
Class XI Chapter 10 - Straight Line

- Page 345 and 346:
Class XI Chapter 10 - Straight Line

- Page 347 and 348:
Class XI Chapter 10 - Straight Line

- Page 349 and 350:
Class XI Chapter 10 - Straight Line

- Page 351 and 352:
Class XI Chapter 10 - Straight Line

- Page 353 and 354:
Class XI Chapter 10 - Straight Line

- Page 355 and 356:
Class XI Chapter 10 - Straight Line

- Page 357 and 358:
Class XI Chapter 10 - Straight Line

- Page 359 and 360:
Class XI Chapter 10 - Straight Line

- Page 361 and 362:
Class XI Chapter 10 - Straight Line

- Page 363 and 364:
Class XI Chapter 10 - Straight Line

- Page 365 and 366:
Class XI Chapter 10 - Straight Line

- Page 367 and 368:
Class XI Chapter 10 - Straight Line

- Page 369 and 370:
Class XI Chapter 10 - Straight Line

- Page 371 and 372:
Class XI Chapter 10 - Straight Line

- Page 373 and 374:
Class XI Chapter 11 - Conic Section

- Page 375 and 376:
Class XI Chapter 11 - Conic Section

- Page 377 and 378:
Class XI Chapter 11 - Conic Section

- Page 379 and 380:
Class XI Chapter 11 - Conic Section

- Page 381 and 382:
Class XI Chapter 11 - Conic Section

- Page 383 and 384:
Class XI Chapter 11 - Conic Section

- Page 385 and 386:
Class XI Chapter 11 - Conic Section

- Page 387 and 388:
Class XI Chapter 11 - Conic Section

- Page 389 and 390:
Class XI Chapter 11 - Conic Section

- Page 391 and 392:
Class XI Chapter 11 - Conic Section

- Page 393 and 394:
Class XI Chapter 11 - Conic Section

- Page 395 and 396:
Class XI Chapter 11 - Conic Section

- Page 397 and 398:
Class XI Chapter 11 - Conic Section

- Page 399 and 400:
Class XI Chapter 11 - Conic Section

- Page 401 and 402:
Class XI Chapter 11 - Conic Section

- Page 403 and 404:
Class XI Chapter 11 - Conic Section

- Page 405 and 406:
Class XI Chapter 11 - Conic Section

- Page 407 and 408:
Class XI Chapter 11 - Conic Section

- Page 409 and 410:
Class XI Chapter 11 - Conic Section

- Page 411 and 412:
Class XI Chapter 11 - Conic Section

- Page 413 and 414:
Class XI Chapter 11 - Conic Section

- Page 415 and 416:
Class XI Chapter 11 - Conic Section

- Page 417 and 418:
Class XI Chapter 12 - Introduction

- Page 419 and 420:
Class XI Chapter 12 - Introduction

- Page 421 and 422:
Class XI Chapter 12 - Introduction

- Page 423 and 424:
Class XI Chapter 12 - Introduction

- Page 425 and 426:
Class XI Chapter 12 - Introduction

- Page 427 and 428:
Class XI Chapter 12 - Introduction

- Page 429 and 430:
Class XI Chapter 12 - Introduction

- Page 431 and 432: Class XI Chapter 13 - Limits and De
- Page 433 and 434: Class XI Chapter 13 - Limits and De
- Page 435 and 436: Class XI Chapter 13 - Limits and De
- Page 437 and 438: Class XI Chapter 13 - Limits and De
- Page 439 and 440: Class XI Chapter 13 - Limits and De
- Page 441 and 442: Class XI Chapter 13 - Limits and De
- Page 443 and 444: Class XI Chapter 13 - Limits and De
- Page 445 and 446: Class XI Chapter 13 - Limits and De
- Page 447 and 448: Class XI Chapter 13 - Limits and De
- Page 449 and 450: Class XI Chapter 13 - Limits and De
- Page 451 and 452: Class XI Chapter 13 - Limits and De
- Page 453 and 454: Class XI Chapter 13 - Limits and De
- Page 455 and 456: Class XI Chapter 13 - Limits and De
- Page 457 and 458: Class XI Chapter 13 - Limits and De
- Page 459 and 460: Class XI Chapter 13 - Limits and De
- Page 461 and 462: Class XI Chapter 13 - Limits and De
- Page 463 and 464: Class XI Chapter 13 - Limits and De
- Page 465 and 466: Class XI Chapter 13 - Limits and De
- Page 467 and 468: Class XI Chapter 13 - Limits and De
- Page 469 and 470: Class XI Chapter 13 - Limits and De
- Page 471 and 472: Class XI Chapter 13 - Limits and De
- Page 473 and 474: Class XI Chapter 13 - Limits and De
- Page 475 and 476: Class XI Chapter 13 - Limits and De
- Page 477 and 478: Class XI Chapter 13 - Limits and De
- Page 479 and 480: Class XI Chapter 13 - Limits and De
- Page 481: Class XI Chapter 13 - Limits and De
- Page 485 and 486: Class XI Chapter 13 - Limits and De
- Page 487 and 488: Class XI Chapter 13 - Limits and De
- Page 489 and 490: Class XI Chapter 13 - Limits and De
- Page 491 and 492: Class XI Chapter 14 - Mathematical
- Page 493 and 494: Class XI Chapter 14 - Mathematical
- Page 495 and 496: Class XI Chapter 14 - Mathematical
- Page 497 and 498: Class XI Chapter 14 - Mathematical
- Page 499 and 500: Class XI Chapter 14 - Mathematical
- Page 501 and 502: Class XI Chapter 14 - Mathematical
- Page 503 and 504: Class XI Chapter 14 - Mathematical
- Page 505 and 506: Class XI Chapter 14 - Mathematical
- Page 507 and 508: Class XI Chapter 15 - Statistics Ma
- Page 509 and 510: Class XI Chapter 15 - Statistics Ma
- Page 511 and 512: Class XI Chapter 15 - Statistics Ma
- Page 513 and 514: Class XI Chapter 15 - Statistics Ma
- Page 515 and 516: Class XI Chapter 15 - Statistics Ma
- Page 517 and 518: Class XI Chapter 15 - Statistics Ma
- Page 519 and 520: Class XI Chapter 15 - Statistics Ma
- Page 521 and 522: Class XI Chapter 15 - Statistics Ma
- Page 523 and 524: Class XI Chapter 15 - Statistics Ma
- Page 525 and 526: Class XI Chapter 15 - Statistics Ma
- Page 527 and 528: Class XI Chapter 15 - Statistics Ma
- Page 529 and 530: Class XI Chapter 15 - Statistics Ma
- Page 531 and 532: Class XI Chapter 15 - Statistics Ma
- Page 533 and 534:
Class XI Chapter 15 - Statistics Ma

- Page 535:
Class XI Chapter 15 - Statistics Ma