Question

y = cos(sin x), find dy/dx​

Answer 1

Answer:

- cos x.sin(sin x)

Explanation:

dy/dx➖ -sin(sin x).cos x

➖ -cos x.sin(sin x)

Answer 2

Given :

$\bf y = \cos(sin \: x)$

To find :

$\bf \: \dfrac{dy}{dx}$

Solution :

$\implies \bf y = \cos(sin \: x)$

Now differentiating both sides :-

$\implies \bf \dfrac{dy}{dx} = \dfrac{d(\cos(sin \: x))}{dx}$

We know that :-

$\underline{ \boxed { \bf\dfrac{d(\cos x)}{dx} = - sin \: x }}$

using Chain rule :-

$\implies \bf \dfrac{dy}{dx} = - \sin(sin \: x) \times \dfrac{d(sin \: x)}{dx} \\ \bf \times \dfrac{dx}{dx}$

We know that :-

$\underline{ \boxed { \bf\dfrac{d(\sin x)}{dx} = cos \: x }}$

$\implies \bf \dfrac{dy}{dx} = - \sin(sin \: x) \times cos \: x \bf \times 1$

$\implies \bf \dfrac{dy}{dx} = -cos \: x \: \sin(sin \: x)$

Answer :

$\bf-cos \: x \: \sin(sin \: x)$