Question

How do you find the derivative of `cos^4(x)-sin^4(x)`?

Answer 1

`f^'(x)=-2sin2x`

Explanation:

Given
`f(x)=(cos^4x-sin^4x)`

`=>f(x)=(cos^2x-sin^2x)(cos^2x+sin^2x)`

`=>f(x)=(cos^2x-sin^2x)*1`

`=>f(x)=cos2x`

Differentiating w.r.to x using chain rule
`=>f^'(x)=d/"dx"(cos2x)=-sin(2x)d/"dx"(2x)`

`=>f^'(x)=-2sin2x`