NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability — Exercise 5.5

Differentiate the functions given in Exercises 1 to 11 w.r.t. x.

Question 1:cos x . cos 2x . cos 3x

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Question 2: ( 1) ( 2) ( 3) ( 4) ( 5) x x x x x − − − − −

Question 3:(log x)cos x

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Question 4:xx – 2sin x

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Question 5:(x + 3)2 . (x + 4)3 . (x + 5)4

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Question 6: 1 1 1 x x x x x    +     +  +

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Question 7:(log x)x + xlog x

Question 8:(sin x)x + sin–1 x

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Question 9:xsin x + (sin x)cos x

Question 10: 2 cos 2 1 1 x x x x x + + −

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Question 11:(x cos x)x + 1 (xsin x) x Find dy dx of the functions given in Exercises 12 to 15

Question 12:xy + yx = 1

Differentiate the functions given in Exercises 1 t

Question 13:yx = xy

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Question 14:(cos x)y = (cos y)x

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Question 15:xy = e(x – y)

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Question 16:Find the derivative of the function given by f (x) = (1 + x) (1 + x2) (1 + x4) (1 + x8) and hence find f ¢(1).

Question 17:Differentiate (x2 – 5x + 8) (x3 + 7x + 9) in three ways mentioned below: (i) by using product rule (ii) by expanding the product to obtain a single polynomial. (iii) by logarithmic differentiation. Do they all give the same answer?

CBSE NCERT Solutions For Class 12 Continuity and Differentiability

Question 18:If u, v and w are functions of x, then show that d dx (u. v. w) = du dx v. w + u . dv dx . w + u . v dw dx in two ways - first by repeated application of product rule, second by logarithmic differentiation.