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Calculus Examples
Step 1
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
Step 2.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.2
Simplify terms.
Step 2.2.1
Combine and .
Step 2.2.2
Cancel the common factor of .
Step 2.2.2.1
Cancel the common factor.
Step 2.2.2.2
Rewrite the expression.
Step 3
Convert from to .
Step 4
Step 4.1
To apply the Chain Rule, set as .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
Replace all occurrences of with .
Step 5
Move to the left of .
Step 6
The derivative of with respect to is .
Step 7
Step 7.1
Reorder the factors of .
Step 7.2
Add parentheses.
Step 7.3
Reorder and .
Step 7.4
Add parentheses.
Step 7.5
Reorder and .
Step 7.6
Reorder and .
Step 7.7
Apply the sine double-angle identity.
Step 7.8
Rewrite in terms of sines and cosines.
Step 7.9
Apply the product rule to .
Step 7.10
One to any power is one.
Step 7.11
Combine and .
Step 7.12
Apply the sine double-angle identity.
Step 7.13
Cancel the common factor of and .
Step 7.13.1
Factor out of .
Step 7.13.2
Cancel the common factors.
Step 7.13.2.1
Factor out of .
Step 7.13.2.2
Cancel the common factor.
Step 7.13.2.3
Rewrite the expression.
Step 7.14
Separate fractions.
Step 7.15
Convert from to .
Step 7.16
Divide by .