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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
Differentiate.
Step 3.2.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.3
Add and .
Step 3.2.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.5
Differentiate using the Power Rule which states that is where .
Step 3.2.6
Multiply by .
Step 3.2.7
By the Sum Rule, the derivative of with respect to is .
Step 3.2.8
Differentiate using the Power Rule which states that is where .
Step 3.2.9
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.10
Differentiate using the Power Rule which states that is where .
Step 3.2.11
Multiply by .
Step 3.2.12
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.13
Add and .
Step 3.3
Simplify.
Step 3.3.1
Apply the distributive property.
Step 3.3.2
Apply the distributive property.
Step 3.3.3
Simplify the numerator.
Step 3.3.3.1
Simplify each term.
Step 3.3.3.1.1
Rewrite using the commutative property of multiplication.
Step 3.3.3.1.2
Multiply by by adding the exponents.
Step 3.3.3.1.2.1
Move .
Step 3.3.3.1.2.2
Multiply by .
Step 3.3.3.1.2.2.1
Raise to the power of .
Step 3.3.3.1.2.2.2
Use the power rule to combine exponents.
Step 3.3.3.1.2.3
Add and .
Step 3.3.3.1.3
Rewrite using the commutative property of multiplication.
Step 3.3.3.1.4
Multiply by by adding the exponents.
Step 3.3.3.1.4.1
Move .
Step 3.3.3.1.4.2
Multiply by .
Step 3.3.3.1.4.2.1
Raise to the power of .
Step 3.3.3.1.4.2.2
Use the power rule to combine exponents.
Step 3.3.3.1.4.3
Add and .
Step 3.3.3.1.5
Multiply by .
Step 3.3.3.1.6
Multiply by .
Step 3.3.3.1.7
Simplify each term.
Step 3.3.3.1.7.1
Multiply by .
Step 3.3.3.1.7.2
Multiply by .
Step 3.3.3.1.8
Expand using the FOIL Method.
Step 3.3.3.1.8.1
Apply the distributive property.
Step 3.3.3.1.8.2
Apply the distributive property.
Step 3.3.3.1.8.3
Apply the distributive property.
Step 3.3.3.1.9
Simplify and combine like terms.
Step 3.3.3.1.9.1
Simplify each term.
Step 3.3.3.1.9.1.1
Multiply by .
Step 3.3.3.1.9.1.2
Multiply by .
Step 3.3.3.1.9.1.3
Rewrite using the commutative property of multiplication.
Step 3.3.3.1.9.1.4
Multiply by by adding the exponents.
Step 3.3.3.1.9.1.4.1
Move .
Step 3.3.3.1.9.1.4.2
Use the power rule to combine exponents.
Step 3.3.3.1.9.1.4.3
Add and .
Step 3.3.3.1.9.1.5
Multiply by .
Step 3.3.3.1.9.1.6
Rewrite using the commutative property of multiplication.
Step 3.3.3.1.9.1.7
Multiply by by adding the exponents.
Step 3.3.3.1.9.1.7.1
Move .
Step 3.3.3.1.9.1.7.2
Multiply by .
Step 3.3.3.1.9.1.7.2.1
Raise to the power of .
Step 3.3.3.1.9.1.7.2.2
Use the power rule to combine exponents.
Step 3.3.3.1.9.1.7.3
Add and .
Step 3.3.3.1.9.1.8
Multiply by .
Step 3.3.3.1.9.2
Subtract from .
Step 3.3.3.2
Add and .
Step 3.3.3.3
Subtract from .
Step 3.3.3.4
Add and .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .