Question

How do you differentiate `f(x)= (1 - sin^2x)/(x-cosx)` using the quotient rule?

Answer 1

`f'(x)=(cos(x)(cos(x)(sin(x)-1)-2xsin(x)))/(x-cos(x))^2`

Explanation:

We have
`f'(x)=(2cos(x)(-sin(x))(x-cos(x)-cos^2(x)(1+sin(x))))/(x-cos(x))^2`

I have used that

`f(x)=cos^2(x)/(x-cos(x))`

since

`1-sin^2(x)=cos^2(x)`