Find the derivatives of the following: (cos x)log x

Find the derivatives of the following:

(cos x)^{log x}

Sum

y = (cos x)^{log x}

Taking log on both sides

log y = log (cos x)^{log x}

log y = (log x) log (cos x)

Differentiating with respect to x

`1/y * ("d"y)/("d"x) = log x xx 1/cosx xx - sin x + log(cosx) xx 1/x`

`1/y ("d"y)/("d"x) = - tan x (log x) + (log(cosx))/x`

`("d"y)/("d"x) = y [(log(cos x))/x - tan x (log x)]`

`("d"y)/("d"x) = (cos x)^(logx) [(log(cos x))/x - tan 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 5 | Page 176

Find the derivatives of the following functions with respect to corresponding independent variables:

y = sin x + cos x

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