Calculus Examples

Find the Derivative - d/dx y = natural log of cos(x)
Step 1
Differentiate using the chain rule, which states that is where and .
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Step 1.1
To apply the Chain Rule, set as .
Step 1.2
The derivative of with respect to is .
Step 1.3
Replace all occurrences of with .
Step 2
Convert from to .
Step 3
The derivative of with respect to is .
Step 4
Simplify.
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Step 4.1
Reorder the factors of .
Step 4.2
Rewrite in terms of sines and cosines.
Step 4.3
Combine and .
Step 4.4
Convert from to .