Question

What is the derivative of `f(t)=cos^2(3t+5)`?

Answer 1

`f'(t)=-6*sin(3t+5)*cos(3t+5)`

Explanation:

`cos^2(3t+5)`
`=cos(3t+5)*cos(3t+5)`

Use product rule:
`=d/dxcos(3t+5)*cos(3t+5)+d/dxcos(3t+5)*cos(3t+5)`

Use the chain rule to differentiate `cos(3t+5)`
`=-sin(3t+5)*3*cos(3t+5)-sin(3t+5)*3*cos(3t+5)`
`=-3*sin(3t+5)*cos(3t+5)-3*sin(3t+5)*cos(3t+5)`

Simplify
`=-6*sin(3t+5)cos(3t+5)`