Answer:
the derivative of given function is
[tex]cos(cos^2 x )(-sin 2 x)[/tex]
Step-by-step explanation:
Step :-
using chain rule formula [tex]\frac{d y}{d x} = \frac{d y}{d u} X\frac{d u}{d x}[/tex]
let [tex]Y = sin(cos^2 x)[/tex] ...........(1)
[tex]\frac{d(sin x)}{d x} = cos x[/tex]
Differentiating equation (1) with respective to x,we get
[tex]\frac{d y}{d x} = cos(cos^2 x) \frac{d}{d x} (cos^2 x)[/tex]........(2)
we will use again formula
[tex]\frac{d(cos x)}{d x} = -sin x[/tex]
[tex]\frac{d (x^{2} )}{d x} =2 x[/tex]
From (2) equation we will get solution is
[tex]\frac{d y}{d x} = cos (cos^2 x) (2 cos x (\frac{d(cos x)}{dx} )[/tex] ........(3)
again simplification the equation (3) we will get
[tex]\frac{d y}{d x} = cos(cos^2 x)(2 cos x(-sin x))[/tex] ........(4)
by using trigonometry formula
[tex]2 sin x cos x = sin2x[/tex]
now the equation (4) we get final solution is
[tex]\frac{d y}{d x} = cos(cos^2 x)(- sin2x)[/tex]
