Find the $\frac{\mathrm{d}y}{\mathrm{d}x}$ of the following functions in terms of $x$: \(y = x^{

Question

Find the $\frac{\mathrm{d}y}{\mathrm{d}x}$ of the following functions in terms of $x$: $y = x^{\sin x}$ $y = x^{\tan x}$ $y = (\cos x)^{\ln x}$

Accepted Answer

(i) $x^{\sin x-1}(\sin x+x\cos x\ln x)$ (ii) $x^{\tan x-1}(\tan x+x\sec^2x\ln x)$ (iii) $(\cos x)^{\ln x}\left(\frac{\ln(\cos x)}x-\tan x\ln x\right)$

Differentiation - Logarithmic Differentiation

Differentiation - Logarithmic Differentiation

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