Question

f( x)=cos(sinx) derivation

Answer 1

$\underline{ \large \purple{{\huge \bf{\dag\:S \mathscr{olution࿐}}}}}$

we need to find derivative of cos x(sin x)

By using product rule for diffrention :

$\underline{ \boxed{ \sf \: f'(x) = u\frac{dv}{dx} + v\frac{du}{dx}}}$

cos x ➔ u

sin x ➔ v

${ \sf \: f'(x) = cos \: x\frac{d(sin \: x)}{dx} + sin \: x\frac{d(cos \: x)}{dx}} \\ \\ \sf \: f'(x) = cos \: x.cos \: x + sin \: x. ( - sin \: x) \\ \\ \sf \: f'(x) = {cos}^{2} x - {sin }^{2} x$

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Answer 2

Solution:

dy/dx = d cos (sinx)/dx

=> dy/dx = - sin (sinx) (cosx)