Find the derivatives of the following:y = xcosx - Mathematics

Find the derivatives of the following:
y = `x^(cosx)`

Sum

y = `x^(cosx)`

Taking log on both sides

log y = log x^{cos x}

log y = cos x log x

Differentiating with respect to x

`1/y * ("d"y)/("d"x) = cosx xx 1/x + (logx)(- sinx)`

`1/y * ("d"y)/("d"x) = 1/x cos x - sin x * log x`

`("d"y)/("d"x) = y[cosx/x - sin x * log x]`

`("d"y)/("d"x) = x^(cosx) [cosx/x - sin x log x]`

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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.4 [Page 176]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.4 | Q 1 | Page 176

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