Question

Find $\frac{dy}{dx}$ if $y=x^2-2^{\sin x}$.

Answer 1

Given,

$y=x^2-2^{\sin x}$

differentiating on both sides, we get,

$\frac{d}{dx}\left(2^{\sin \left(x\right)}\right)$

$=\frac{d}{dx}\left(e^{\sin \left(x\right)\ln \left(2\right)}\right)$

$=\ln \left(2\right)\cdot 2^{\sin \left(x\right)}\cos \left(x\right)$

$\frac{dy}{dx}=2x-\ln \left(2\right)\cdot 2^{\sin \left(x\right)}\cos \left(x\right)$