CLASS_11_MATHS_SOLUTIONS_NCERT

Recommendations

Info

Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ Question 24: 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): (ax 2 + sin x) (p + q cos x) Solution 24: Let f x ax 2 sin x (p + q cos x) By product rule, d d f ' x ax sin x p qcos x p qcos x ax sin x dx dx 2 2 2 ax sin x qsin x p qcos x2ax cos x 2 qsin x ax sin x p qcos x 2ax cos x Question 25: 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 + cos x) (x – tan x) Solution 25: Let f(x) = (x + cos x) (x – tan x) By product rule, d d f ' x (x + cos x) x tan xx tan x x cos x dx dx d d x + cos x x tan x x tan x1 sin x dx dx d x + cos x1 tan x x tan x1 sin x ... i dx Let g x tan x. Accordingly, g(x+h)=tan x+h By first principle, gx hg x g' x lim h0 h tan x htan x lim h0 h lim 1 sin( x h) sin x h0 h cos x h cos x 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 ______________________________________________________________________________ 1 sin( x h)cos x sin xcos x h lim h0 h cos x hcos x 1 1 sin( x h x) lim cos x h0 h cos x h 1 1 sinh lim cos x h0 h cos x h 1 sinh 1 . lim . lim cos x h0 h h0 cos x h 1 1 .1. cos x cos x0 1 2 cos x 2 sec x ii x x 2 x x x x Therefore, from (i) and ii ,We obtain f' x cos (1 sec ) tan 1 sin 2 x cos x tan x x tan x1 sin x 2 tan x x cos x x tan x 1sin x Question 26: 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): Solution 26: Let f(x) = 4 x 5sin x 3x7cos x By quotient rule, f ' x d dx 4x5sin x 3x7cos x 3x 7cos x 4x 5sin x4x 5sin x 3x 7cos x 3x7cos x 2 d dx 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:
Page 5 and 6:
Page 7 and 8:
Page 9 and 10:
Page 11 and 12:
Page 13 and 14:
Page 15 and 16:
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Class XI Chapter 2 - Relations and
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
Class XI Chapter 3 - Trigonometric
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Class XI Chapter 4 - Principle of M
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Class XI Chapter 5 - Complex Number
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Class XI Chapter 6 - Linear Inequal
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Class XI Chapter 7 - Permutation an
Page 199 and 200:
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
Class XI Chapter 8 - Binomial Theor
Page 221 and 222:
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Class XI Chapter 9 - Sequences and
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
Page 285 and 286:
Page 287 and 288:
Page 289 and 290:
Page 291 and 292:
Page 293 and 294:
Page 295 and 296:
Page 297 and 298:
Page 299 and 300:
Page 301 and 302:
Page 303 and 304:
Page 305 and 306:
Page 307 and 308:
Page 309 and 310:
Page 311 and 312:
Page 313 and 314:
Class XI Chapter 10 - Straight Line
Page 315 and 316:
Page 317 and 318:
Page 319 and 320:
Page 321 and 322:
Page 323 and 324:
Page 325 and 326:
Page 327 and 328:
Page 329 and 330:
Page 331 and 332:
Page 333 and 334:
Page 335 and 336:
Page 337 and 338:
Page 339 and 340:
Page 341 and 342:
Page 343 and 344:
Page 345 and 346:
Page 347 and 348:
Page 349 and 350:
Page 351 and 352:
Page 353 and 354:
Page 355 and 356:
Page 357 and 358:
Page 359 and 360:
Page 361 and 362:
Page 363 and 364:
Page 365 and 366:
Page 367 and 368:
Page 369 and 370:
Page 371 and 372:
Page 373 and 374:
Class XI Chapter 11 - Conic Section
Page 375 and 376:
Page 377 and 378:
Page 379 and 380:
Page 381 and 382:
Page 383 and 384:
Page 385 and 386:
Page 387 and 388:
Page 389 and 390:
Page 391 and 392:
Page 393 and 394:
Page 395 and 396:
Page 397 and 398:
Page 399 and 400:
Page 401 and 402:
Page 403 and 404:
Page 405 and 406:
Page 407 and 408:
Page 409 and 410:
Page 411 and 412:
Page 413 and 414:
Page 415 and 416:
Page 417 and 418:
Class XI Chapter 12 - Introduction
Page 419 and 420:
Page 421 and 422:
Page 423 and 424:
Page 425 and 426:
Page 427 and 428:
Page 429 and 430:
Page 431 and 432:
Class XI Chapter 13 - Limits and De
Page 433 and 434: Class XI Chapter 13 - Limits and De
Page 483: Class XI Chapter 13 - Limits and De
Page 491 and 492: Class XI Chapter 14 - Mathematical
Page 507 and 508: Class XI Chapter 15 - Statistics Ma
Page 535:
Class XI Chapter 15 - Statistics Ma
show all

CLASS_11_MATHS_SOLUTIONS_NCERT

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?