Calculus Examples

Find the Derivative - d/dx 7 natural log of sec(x)+tan(x)
Step 1
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the chain rule, which states that is where and .
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Step 2.1
To apply the Chain Rule, set as .
Step 2.2
The derivative of with respect to is .
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate using the Sum Rule.
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Step 3.1
Combine and .
Step 3.2
By the Sum Rule, the derivative of with respect to is .
Step 4
The derivative of with respect to is .
Step 5
The derivative of with respect to is .
Step 6
Simplify.
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Step 6.1
Reorder the factors of .
Step 6.2
Apply the distributive property.
Step 6.3
Multiply .
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Step 6.3.1
Combine and .
Step 6.3.2
Combine and .
Step 6.4
Combine and .
Step 6.5
Move to the left of .
Step 6.6
Combine the numerators over the common denominator.
Step 6.7
Factor out of .
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Step 6.7.1
Factor out of .
Step 6.7.2
Factor out of .
Step 6.7.3
Factor out of .