To determine

To find: The derivative of y

Answer

y'=cosx4 x sin⁡x

Explanation

Formula:

i.

Radical rule,ddxx= 12x

ii.

Chain rule,ddx(fgx=f'gx*g'(x)

iii.

Trigonometric rule,ddx(sin⁡x)=cos⁡x

Given:

y= sin⁡x

Calculation:

Consider the given function y= sin⁡x

Differentiate with respect to x on both sides

ddxy=ddxsin⁡x

Applying the radical and chain rule of differentiation

y'=12sin⁡x*ddx(sin⁡x )

By applying the trigonometric and chain rule of differentiation

y'=12sin⁡x*cos⁡x*ddx(x)

y'=12sin⁡x*cos⁡x*12x

y'=cosx4x*sin⁡x

y'=cosx4x  sin⁡x

Conclusion:

y'=cosx4x  sin⁡x