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

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Answer 1 · 2016-03-05T21:05:25

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

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.

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