Question

Find the derivative of cos x square - sin 2x raise to 5

Answer 1

$\boxed{\textbf{\large{Step-by-step explanation:}}}$

Given function is

$y = ( \cos( {x}^{2} ) - \sin( {2x}^{5} )$

Differentiation wrt x

$\frac{dy}{dx} = \frac{d}{dx}( \cos( {x}^{2} ) - \sin( {(2x}^{5} ) )$

$= - \sin( {x}^{2} ) \times \frac{d}{dx} ( {x}^{2} ) \\ \: \: \: \: \: \: \: - \cos( {2x}^{5} \times \frac{d}{dx} ( {2x}^{5}$

$= - \sin( {x}^{2} ) \times 2x - \cos( {2x}^{5} ) \times 10 {x}^{4}$

$= - ( 2x\sin( {x}^{2} ) + 10 {x}^{4} \cos(2 {x}^{5} ) )$

$= - \sin( {x}^{2} ) \times 2x - \cos( {(2x}^{5} ) \times 10 {x}^{4}$

$= - (2x) \sin( {x}^{2} ) - (10 {x}^{4} )\cos( {(2x}^{5} )$

$= -2 ( x\sin( {x}^{2} ) + 5 {x}^{4} \cos(2 {x}^{5} ) )$

$\frac{dy}{dx}=-2( x\sin( {x}^{2} )+ 5 {x}^{4} \cos(2 {x}^{5} ) )$