Derivative of (cosx)(sinx)(tanx)

Question

f(x)= (cosx)(sinx)(tanx) 

 

I am stuck om this problem. Please show me steps on how to go about solving this. 

Answer 1

Write tan(x) so that it is terms of sin(x) and cos(x).

 

f(x) = cos(x)sin(x)[sin(x) / cos(x)]

 

f(x) = sin²(x)

 

 

So now you just take the derivative of sin²(x) using the chain rule.

Answer 2

f(x) = cos x * sin x * ( sin x / cos x ) 

 

 

= sin ^ 2 x

 

using the chain rule 

 

 

f'(x) = 2 sin x * cos x 

 

= 2 sin x cos x