Differentiate both sides of the equation.

The derivative of with respect to is .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

The derivative of with respect to is .

Replace all occurrences of with .

Convert from to .

The derivative of with respect to is .

Simplify the expression.

Move to the left of .

Rewrite as .

Reform the equation by setting the left side equal to the right side.

Rewrite in terms of sines and cosines.

Combine and .

Convert from to .

Replace with .

Find dy/dx y = natural log of cos(x)