Question

Differentiate
\[\ln \sin^2 x\]

Answer 1

take sin^2x = t.

dt/dx = 2sinx cosx = sin2x

now for y=lnt
dy/dx = 1/t dt/dx
= 1/sin^2x . 2sinx cosx
= cosx/sinx
=cotx

Answer 2

sorry its 2cotx.

Answer 3

Like your last problem, it is work you using some properties of logarithms to simply the problem.

As
\[ \ln y^2 = 2 \ln y, \] it follows that
\[ \ln \sin^2 x = 2 \ln \sin x \]

Now this function is a little easier to differentiate.

Answer 4

thanks