Question

Differentiate w.r.t. x
d cos(sinx²)/dx

Answer 1

Answer :

Let, y = cos(sinx²)

Now, differentiating both sides with respect to x, we get

$\frac{dy}{dx} = \frac{d}{dx} cos(sin \: {x}^{2} ) \\ \\ = - sin(sin \: {x}^{2} ) \: \frac{d}{dx} (sin \: {x}^{2} ) \\ \\ = - (sin(sin \: {x}^{2} )) \:( cos \: {x}^{2} ) \: \frac{d}{dx} ( {x}^{2} ) \\ \\ = - (sin(sin \: {x}^{2} )) \:( cos \: {x}^{2} ) \: (2x) \\ \\ = - 2x \: (cos \: {x}^{2} )(sin(sin \: {x}^{2} )),$

which is the required derivative.

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