Use logarthmjc differentiation to find the derivative of the function y=x^sin (x)

Question

Tabitha

Mathematics

23 August, 13:32

Use logarthmjc differentiation to find the derivative of the function y=x^sin (x)

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Craig Huber · Answer 1

dy/dx = x^sin (x) * (sin (x) / x + cos (x) * lnx)

Step-by-step explanation:

∵ y = x^sin (x)

∴㏑y = ㏑ (x^sin (x)) = sinx * ㏑x - - - by differentiating both sides with respect to x

(1/y) * dy/dx = sin (x) / x + cos (x) lnx

dy/dx = x^sin (x) * (sin (x) / x + cos (x) * lnx)