Answer:
Step-by-step explanation:
I'm assuming you want to find the derivative of the function y = ln (sin x).
If this is the case, let's look at the derivatives of y = ln x and y = sin x separately and then use the results as appropriate:
(d/dx) ln x = 1/x
(d/dx) ln u = (1/u)(du/dx)
(d/dx) sin x = cos x
We'll also need to use the Chain Rule (which we have done in finding the derivative of ln u, above).
1 1 cos x
(d/dx) ln (sin x) = ------------- * (d/dx) (sin x) = ----------- * cos x = ------------ = cot x
sin x sin x sin x
