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Calculus Examples
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
The derivative of with respect to is .
Step 3
The derivative of with respect to is .
Step 4
Step 4.1
Reorder terms.
Step 4.2
Simplify each term.
Step 4.2.1
Rewrite in terms of sines and cosines.
Step 4.2.2
Multiply .
Step 4.2.2.1
Combine and .
Step 4.2.2.2
Raise to the power of .
Step 4.2.2.3
Raise to the power of .
Step 4.2.2.4
Use the power rule to combine exponents.
Step 4.2.2.5
Add and .
Step 4.2.3
Rewrite in terms of sines and cosines.
Step 4.2.4
Apply the product rule to .
Step 4.2.5
Cancel the common factor of .
Step 4.2.5.1
Move the leading negative in into the numerator.
Step 4.2.5.2
Factor out of .
Step 4.2.5.3
Cancel the common factor.
Step 4.2.5.4
Rewrite the expression.
Step 4.2.6
One to any power is one.
Step 4.2.7
Multiply by .
Step 4.2.8
Move the negative in front of the fraction.
Step 4.3
Combine the numerators over the common denominator.
Step 4.4
Reorder and .
Step 4.5
Rewrite as .
Step 4.6
Factor out of .
Step 4.7
Factor out of .
Step 4.8
Rewrite as .
Step 4.9
Apply pythagorean identity.
Step 4.10
Cancel the common factor of and .
Step 4.10.1
Factor out of .
Step 4.10.2
Cancel the common factors.
Step 4.10.2.1
Multiply by .
Step 4.10.2.2
Cancel the common factor.
Step 4.10.2.3
Rewrite the expression.
Step 4.10.2.4
Divide by .