Calculus Examples

Find the Derivative - d/dx natural log of 4sec(x)
Step 1
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
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
Differentiate using the Constant Multiple Rule.
Tap for more steps...
Step 2.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.2
Simplify terms.
Tap for more steps...
Step 2.2.1
Combine and .
Step 2.2.2
Cancel the common factor of .
Tap for more steps...
Step 2.2.2.1
Cancel the common factor.
Step 2.2.2.2
Rewrite the expression.
Step 3
Rewrite in terms of sines and cosines.
Step 4
Multiply by the reciprocal of the fraction to divide by .
Step 5
Multiply by .
Step 6
The derivative of with respect to is .
Step 7
Simplify.
Tap for more steps...
Step 7.1
Rewrite in terms of sines and cosines, then cancel the common factors.
Tap for more steps...
Step 7.1.1
Reorder and .
Step 7.1.2
Rewrite in terms of sines and cosines.
Step 7.1.3
Cancel the common factors.
Step 7.2
Multiply by .
Step 7.3
Rewrite in terms of sines and cosines.
Step 7.4
Convert from to .