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Calculus Examples
Step 1
Differentiate both sides of the equation.
Step 2
The derivative of with respect to is .
Step 3
Step 3.1
Differentiate using the Product Rule which states that is where and .
Step 3.2
The derivative of with respect to is .
Step 3.3
Raise to the power of .
Step 3.4
Raise to the power of .
Step 3.5
Use the power rule to combine exponents.
Step 3.6
Add and .
Step 3.7
The derivative of with respect to is .
Step 3.8
Raise to the power of .
Step 3.9
Raise to the power of .
Step 3.10
Use the power rule to combine exponents.
Step 3.11
Add and .
Step 3.12
Simplify.
Step 3.12.1
Reorder and .
Step 3.12.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 3.12.3
Expand using the FOIL Method.
Step 3.12.3.1
Apply the distributive property.
Step 3.12.3.2
Apply the distributive property.
Step 3.12.3.3
Apply the distributive property.
Step 3.12.4
Combine the opposite terms in .
Step 3.12.4.1
Reorder the factors in the terms and .
Step 3.12.4.2
Add and .
Step 3.12.4.3
Add and .
Step 3.12.5
Simplify each term.
Step 3.12.5.1
Multiply .
Step 3.12.5.1.1
Raise to the power of .
Step 3.12.5.1.2
Raise to the power of .
Step 3.12.5.1.3
Use the power rule to combine exponents.
Step 3.12.5.1.4
Add and .
Step 3.12.5.2
Rewrite using the commutative property of multiplication.
Step 3.12.5.3
Multiply .
Step 3.12.5.3.1
Raise to the power of .
Step 3.12.5.3.2
Raise to the power of .
Step 3.12.5.3.3
Use the power rule to combine exponents.
Step 3.12.5.3.4
Add and .
Step 3.12.6
Apply the cosine double-angle identity.
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .