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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
Raise to the power of .
Step 4
Raise to the power of .
Step 5
Use the power rule to combine exponents.
Step 6
Add and .
Step 7
The derivative of with respect to is .
Step 8
Raise to the power of .
Step 9
Raise to the power of .
Step 10
Use the power rule to combine exponents.
Step 11
Add and .
Step 12
Step 12.1
Reorder and .
Step 12.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 12.3
Expand using the FOIL Method.
Step 12.3.1
Apply the distributive property.
Step 12.3.2
Apply the distributive property.
Step 12.3.3
Apply the distributive property.
Step 12.4
Combine the opposite terms in .
Step 12.4.1
Reorder the factors in the terms and .
Step 12.4.2
Add and .
Step 12.4.3
Add and .
Step 12.5
Simplify each term.
Step 12.5.1
Multiply .
Step 12.5.1.1
Raise to the power of .
Step 12.5.1.2
Raise to the power of .
Step 12.5.1.3
Use the power rule to combine exponents.
Step 12.5.1.4
Add and .
Step 12.5.2
Rewrite using the commutative property of multiplication.
Step 12.5.3
Multiply .
Step 12.5.3.1
Raise to the power of .
Step 12.5.3.2
Raise to the power of .
Step 12.5.3.3
Use the power rule to combine exponents.
Step 12.5.3.4
Add and .
Step 12.6
Apply the cosine double-angle identity.