Q16 of 147 Page 178

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

Given: f (x) = (1 + x) (1 + x2) (1 + x4) (1 + x8)

Taking log on both sides, we get


log f (x) =log (1 + x) + log (1 + x2) + log (1 + x4) + log (1 + x8)


Now, differentiate both sides with respect to x











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14

Find dy/dx of the functions.

(cos x)y = (cos y)x

 15

Find dy/dx of the functions.

xy = e(x – y)

 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?

 18

If u, v and w are functions of x, then show that


in two ways – first by repeated application of product rule, second by logarithmic differentiation.