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

1 Answer
Mar 5, 2016

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.