Question

$\bf \large \pink {Namaste} \: \blue{ Maths} \: \purple{ Experts}$
$\sf Find \: \frac{dy}{dx}$
$\sf \: if \: y = {sin \: x}^{(log \: x)}$
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Answer 1

Answer:

$y = { (\sin \: x )}^{ logx} \\ taking \: log \: both \: side \: \\ log \: y = log \: x( log \: \sin \: x)$

$Differentiate \: on \: both \: sides$

$\frac{1}{y} \times \frac{dy}{dx} = \frac{ log \: x }{ \sin \: x \times \cos \: x } + { log \: \sin \: x} \times \frac{1}{x}$

$hence$

$\frac{dy}{dx} = { \sin \: x }^{ log \: x( log \: x \: \times \cot \: x + \frac{ log \: \sin \: x}{x}) }$