derivative w(x) = 2cotx sin^2x

Question

the derivative of w(x) = 2cotx sin^2x

Answer 1

Rewrite the function to simplify.

 

w(x) = 2(cosx/sinx)(sin²x)

w(x) = 2sinxcosx

 

Realize that this is a double-angle formula for sine.

 

w(x) = sin(2x)

 

Use the chain rule to derivative.

 

[d/dx]w(x) = 2cos(2x)

Answer 2

w(x) = 2 cot x sin² x = 2 cos x sin x = sin 2x

 

dw/dx = 2 cos 2x