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

Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
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.
Simplify.
Rewrite in terms of sines and cosines.
Combine and .
Convert from to .
Replace with .
Find dy/dx y = natural log of cos(x)

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