Question

How do I find the derivative of `log(sin^2(x))`?

Answer 1

First write `log(sin^2(x)) = 2log(sin(x))`

Explanation:

Assuming that we are using `log` for `log_10` (the common logarithm).

`d/dx(logu) = 1/(u ln10) d/dx(u)`

So we get

`d/dx(2log(sin(x))) = 2/(sinx ln10) d/dx(sinx)`

`= 2/(sinx ln10) cosx`

`= (2cotx)/ln10`

If `log` is being used for the natural logarithm , get rid of the `ln10` in the answers above.