Calculus Examples

Find the Derivative - d/dx y=sec(sin(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
The derivative of with respect to is .
Step 3
Simplify.
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Step 3.1
Reorder the factors of .
Step 3.2
Rewrite in terms of sines and cosines.
Step 3.3
Combine and .
Step 3.4
Rewrite in terms of sines and cosines.
Step 3.5
Multiply .
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Step 3.5.1
Multiply by .
Step 3.5.2
Raise to the power of .
Step 3.5.3
Raise to the power of .
Step 3.5.4
Use the power rule to combine exponents.
Step 3.5.5
Add and .
Step 3.6
Factor out of .
Step 3.7
Separate fractions.
Step 3.8
Rewrite as a product.
Step 3.9
Write as a fraction with denominator .
Step 3.10
Simplify.
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Step 3.10.1
Divide by .
Step 3.10.2
Convert from to .
Step 3.11
Convert from to .