Question

How do you find the derivative of `sin^2 (2x+3)`?

Answer 1

`4sin(2x+3)cos(2x+3)`

Explanation:

According to the chain rule:

`f'(x)=2sin(2x+3)d/dx[sin(2x+3)]`

Now, find that derivative.
`d/dx[sin(2x+3)]=cos(2x+3)overbrace(d/dx[2x+3])^(color(red)(=2))=2cos(2x+3)`

Plug this back in.

`f'(x)=4sin(2x+3)cos(2x+3)`