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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
Apply the product rule to .
Step 4.2.3
Cancel the common factor of .
Step 4.2.3.1
Factor out of .
Step 4.2.3.2
Cancel the common factor.
Step 4.2.3.3
Rewrite the expression.
Step 4.2.4
One to any power is one.
Step 4.2.5
Rewrite in terms of sines and cosines.
Step 4.2.6
Multiply .
Step 4.2.6.1
Combine and .
Step 4.2.6.2
Raise to the power of .
Step 4.2.6.3
Raise to the power of .
Step 4.2.6.4
Use the power rule to combine exponents.
Step 4.2.6.5
Add and .
Step 4.3
Combine the numerators over the common denominator.
Step 4.4
Apply pythagorean identity.
Step 4.5
Cancel the common factor of and .
Step 4.5.1
Factor out of .
Step 4.5.2
Cancel the common factors.
Step 4.5.2.1
Multiply by .
Step 4.5.2.2
Cancel the common factor.
Step 4.5.2.3
Rewrite the expression.
Step 4.5.2.4
Divide by .