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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 Quotient Rule which states that is where and .
Step 3.2
The derivative of with respect to is .
Step 3.3
Differentiate.
Step 3.3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.3
Add and .
Step 3.4
The derivative of with respect to is .
Step 3.5
Raise to the power of .
Step 3.6
Raise to the power of .
Step 3.7
Use the power rule to combine exponents.
Step 3.8
Add and .
Step 3.9
Simplify.
Step 3.9.1
Apply the distributive property.
Step 3.9.2
Simplify the numerator.
Step 3.9.2.1
Simplify each term.
Step 3.9.2.1.1
Multiply by .
Step 3.9.2.1.2
Rewrite using the commutative property of multiplication.
Step 3.9.2.1.3
Multiply .
Step 3.9.2.1.3.1
Raise to the power of .
Step 3.9.2.1.3.2
Raise to the power of .
Step 3.9.2.1.3.3
Use the power rule to combine exponents.
Step 3.9.2.1.3.4
Add and .
Step 3.9.2.2
Factor out of .
Step 3.9.2.3
Factor out of .
Step 3.9.2.4
Factor out of .
Step 3.9.2.5
Apply pythagorean identity.
Step 3.9.2.6
Multiply by .
Step 3.9.3
Combine terms.
Step 3.9.3.1
Cancel the common factor of and .
Step 3.9.3.1.1
Factor out of .
Step 3.9.3.1.2
Rewrite as .
Step 3.9.3.1.3
Factor out of .
Step 3.9.3.1.4
Rewrite as .
Step 3.9.3.1.5
Reorder terms.
Step 3.9.3.1.6
Factor out of .
Step 3.9.3.1.7
Cancel the common factors.
Step 3.9.3.1.7.1
Factor out of .
Step 3.9.3.1.7.2
Cancel the common factor.
Step 3.9.3.1.7.3
Rewrite the expression.
Step 3.9.3.2
Move the negative in front of the fraction.
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .