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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
Multiply the exponents in .
Step 3.2.1
Apply the power rule and multiply exponents, .
Step 3.2.2
Multiply by .
Step 3.3
Differentiate using the Product Rule which states that is where and .
Step 3.4
Differentiate.
Step 3.4.1
By the Sum Rule, the derivative of with respect to is .
Step 3.4.2
Differentiate using the Power Rule which states that is where .
Step 3.4.3
Since is constant with respect to , the derivative of with respect to is .
Step 3.4.4
Differentiate using the Power Rule which states that is where .
Step 3.4.5
Multiply by .
Step 3.4.6
Since is constant with respect to , the derivative of with respect to is .
Step 3.4.7
Add and .
Step 3.4.8
By the Sum Rule, the derivative of with respect to is .
Step 3.4.9
Differentiate using the Power Rule which states that is where .
Step 3.4.10
Since is constant with respect to , the derivative of with respect to is .
Step 3.4.11
Simplify the expression.
Step 3.4.11.1
Add and .
Step 3.4.11.2
Multiply by .
Step 3.4.12
Differentiate using the Power Rule which states that is where .
Step 3.4.13
Simplify with factoring out.
Step 3.4.13.1
Multiply by .
Step 3.4.13.2
Factor out of .
Step 3.4.13.2.1
Factor out of .
Step 3.4.13.2.2
Factor out of .
Step 3.4.13.2.3
Factor out of .
Step 3.5
Cancel the common factors.
Step 3.5.1
Factor out of .
Step 3.5.2
Cancel the common factor.
Step 3.5.3
Rewrite the expression.
Step 3.6
Simplify.
Step 3.6.1
Apply the distributive property.
Step 3.6.2
Apply the distributive property.
Step 3.6.3
Simplify the numerator.
Step 3.6.3.1
Simplify each term.
Step 3.6.3.1.1
Expand using the FOIL Method.
Step 3.6.3.1.1.1
Apply the distributive property.
Step 3.6.3.1.1.2
Apply the distributive property.
Step 3.6.3.1.1.3
Apply the distributive property.
Step 3.6.3.1.2
Simplify and combine like terms.
Step 3.6.3.1.2.1
Simplify each term.
Step 3.6.3.1.2.1.1
Rewrite using the commutative property of multiplication.
Step 3.6.3.1.2.1.2
Multiply by by adding the exponents.
Step 3.6.3.1.2.1.2.1
Move .
Step 3.6.3.1.2.1.2.2
Multiply by .
Step 3.6.3.1.2.1.3
Move to the left of .
Step 3.6.3.1.2.1.4
Multiply by .
Step 3.6.3.1.2.1.5
Multiply by .
Step 3.6.3.1.2.2
Subtract from .
Step 3.6.3.1.3
Apply the distributive property.
Step 3.6.3.1.4
Simplify.
Step 3.6.3.1.4.1
Rewrite using the commutative property of multiplication.
Step 3.6.3.1.4.2
Rewrite using the commutative property of multiplication.
Step 3.6.3.1.4.3
Move to the left of .
Step 3.6.3.1.5
Simplify each term.
Step 3.6.3.1.5.1
Multiply by by adding the exponents.
Step 3.6.3.1.5.1.1
Move .
Step 3.6.3.1.5.1.2
Multiply by .
Step 3.6.3.1.5.1.2.1
Raise to the power of .
Step 3.6.3.1.5.1.2.2
Use the power rule to combine exponents.
Step 3.6.3.1.5.1.3
Add and .
Step 3.6.3.1.5.2
Multiply by by adding the exponents.
Step 3.6.3.1.5.2.1
Move .
Step 3.6.3.1.5.2.2
Multiply by .
Step 3.6.3.1.6
Multiply by by adding the exponents.
Step 3.6.3.1.6.1
Multiply by .
Step 3.6.3.1.6.1.1
Raise to the power of .
Step 3.6.3.1.6.1.2
Use the power rule to combine exponents.
Step 3.6.3.1.6.2
Add and .
Step 3.6.3.1.7
Rewrite using the commutative property of multiplication.
Step 3.6.3.1.8
Multiply by by adding the exponents.
Step 3.6.3.1.8.1
Move .
Step 3.6.3.1.8.2
Multiply by .
Step 3.6.3.1.9
Move to the left of .
Step 3.6.3.1.10
Multiply by .
Step 3.6.3.1.11
Expand by multiplying each term in the first expression by each term in the second expression.
Step 3.6.3.1.12
Combine the opposite terms in .
Step 3.6.3.1.12.1
Reorder the factors in the terms and .
Step 3.6.3.1.12.2
Add and .
Step 3.6.3.1.12.3
Add and .
Step 3.6.3.1.13
Simplify each term.
Step 3.6.3.1.13.1
Multiply by by adding the exponents.
Step 3.6.3.1.13.1.1
Move .
Step 3.6.3.1.13.1.2
Multiply by .
Step 3.6.3.1.13.1.2.1
Raise to the power of .
Step 3.6.3.1.13.1.2.2
Use the power rule to combine exponents.
Step 3.6.3.1.13.1.3
Add and .
Step 3.6.3.1.13.2
Rewrite using the commutative property of multiplication.
Step 3.6.3.1.13.3
Multiply by by adding the exponents.
Step 3.6.3.1.13.3.1
Move .
Step 3.6.3.1.13.3.2
Multiply by .
Step 3.6.3.1.13.4
Multiply by .
Step 3.6.3.1.13.5
Multiply by .
Step 3.6.3.1.14
Combine the opposite terms in .
Step 3.6.3.1.14.1
Add and .
Step 3.6.3.1.14.2
Add and .
Step 3.6.3.2
Combine the opposite terms in .
Step 3.6.3.2.1
Add and .
Step 3.6.3.2.2
Add and .
Step 3.6.3.2.3
Add and .
Step 3.6.3.2.4
Add and .
Step 3.6.3.3
Add and .
Step 3.6.3.4
Subtract from .
Step 3.6.3.5
Add and .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .