Q15 of 147 Page 178

Find dy/dx of the functions.

xy = e(x – y)

Given: xy = e(x – y)

Taking log on both sides, we get


log (xy) = log (e(x – y))


⇒ log x + log y = (x - y) log e


⇒ log x + log y = (x - y) .1


⇒ log x + log y = (x - y)


Now, differentiate both sides with respect to x







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13

Find dy/dx of the functions.

yx = xy

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Find dy/dx of the functions.

(cos x)y = (cos y)x

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

 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?