Question

find dy/dx if y = x^cos x + e^sin x​

Answer 1

Step-by-step explanation:

We have,

$y = {x}^{ \cos(x) } + {e}^{ \sin(x) }$

$\implies \frac{dy}{dx} = {x}^{ \cos(x) } ( \frac{d}{dx} ( \cos(x) ln(x) )) + {e}^{ \sin(x) } . \cos(x)$

$\implies \frac{dy}{dx} = {x}^{ \cos(x) } ( - \sin(x) ln(x) + \cos(x) . \frac{1}{x} ) + {e}^{ \sin(x) } . \cos(x)$

$\implies \frac{dy}{dx} = - {x}^{ \cos(x) } . \sin(x) . ln(x) + {x}^{( \cos(x) - 1) } . \cos(x) + {e}^{ \sin(x) } . \cos(x)$