Diff $(sin x)^{cos x}$ wrt $x$ .

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Solution

$y = (s i n x)^{c o s x}$

$l o g y = c o s x \times log s i n x$

$\frac{1}{y} \frac{d y}{d x} = - s i n x \times log s i n x + \frac{c o s x}{s i n x} \times c o s x$

Hence $\frac{d y}{d x} = s i n x^{c o s x} (- s i n x \times log s i n x + \frac{c o s^{2} x}{s i n x})$

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