Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ d sec x sec x ...iii dx From (i), (ii), and (iii), we obtain 2 f ' x x sec x 1 sec x x tan x 1 sec xtan x Question 30: Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s x are fixed non-zero constants and m and n are integers): sin n x Solution 30: x Let f(x) = sin n x By quotient rule, d n d n sin x x x sin x f ' x dx dx 2n sin x d n n1 It can be easily shown that sin x nsin xcos x dx Therefore, n d d n sin x x x sin x f ' x dx dx 2n sin x n n1 sin x.1 xnsin xcos x 2n sin x n1 sin xsin x nx cos x 2n sin x sin x nx cos x n1 sin x Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 14 – Mathematical Reasoning Maths ______________________________________________________________________________ Exercise 14.1 Book Name: **NCERT** Solutions Question 1: Which of the following sentences are statements? Give reasons for your answer. (i) There are 35 days in a month. (ii) Mathematics is difficult. (iii) The sum of 5 and 7 is greater than 10. (iv) The square of a number is an even number. (v) The sides of a quadrilateral have equal length. (vi) Answer this question. (vii) The product of (-1) and 8 is 8. (viii) The sum of all interior angles of a triangle is 180Â°. (ix) Today is a windy day. (x) All real numbers are complex numbers. Solution 1: (i) This sentence is incorrect because the maximum number of days in a month is 31. Hence, it is a statement. (ii) This sentence is subjective in the sense that for some people, mathematics can be easy and for some others, it can be difficult. Hence, it is not a statement. (iii) The sum of 5 and 7 is 12, which is greater than 10. Therefore, this sentence is always correct. Hence, it is a statement. (iv) This sentence is sometimes correct and sometimes incorrect. For example, the square of 2 is an even number. However, the square of 3 is an odd number. Hence, it is not a statement. (v) This sentence is sometimes correct and sometimes incorrect. For example, squares and rhombus have sides of equal lengths. However, trapezium and rectangles have sides of unequal lengths. Hence, it is not a statement. (vi) It is an order. Therefore, it is not a statement. (vii) The product of (-1) and 8 is (-8). Therefore, the given sentence is incorrect. Hence, it is a statement. (viii) This sentence is correct and hence, it is a statement. (ix) The day that is being referred to is not evident from the sentence. Hence, it is not a statement. (x) All real numbers can be written as a Ã— 1 + 0 Ã— i. Therefore, the given sentence is always correct. Hence, it is a statement. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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