Question

what is derivative of cos (sin x)

Answer 1

Dear student,

$$\begin{gathered} \frac{d}{dx}\cos (\sin (x)) \\ Us\mathrm{in}gchainrule,\frac{dy}{dx}=\frac{dy}{du}\cdot \frac{du}{dx},letu=\sin (x) \\ \frac{dy}{du}=\frac{d}{du}\cos u=-\sin u=-\sin (\sin (x)) \\ \frac{du}{dx}=\frac{d}{dx}=\sin \left(x\right)=\cos (x) \\ \therefore \frac{dy}{dx}=-\sin (\sin (x))\cdot \cos (x)=-\sin (\sin (x))\cos (x) \end{gathered}$$

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