Calculus Examples

Find the Derivative - d/dx y = natural log of sec(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
Rewrite in terms of sines and cosines.
Step 3
Multiply by the reciprocal of the fraction to divide by .
Step 4
Multiply by .
Step 5
The derivative of with respect to is .
Step 6
Simplify.
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Step 6.1
Rewrite in terms of sines and cosines, then cancel the common factors.
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Step 6.1.1
Reorder and .
Step 6.1.2
Rewrite in terms of sines and cosines.
Step 6.1.3
Cancel the common factors.
Step 6.2
Multiply by .
Step 6.3
Rewrite in terms of sines and cosines.
Step 6.4
Convert from to .