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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
Multiply the exponents in .
Step 3.2.1.1
Apply the power rule and multiply exponents, .
Step 3.2.1.2
Multiply by .
Step 3.2.2
By the Sum Rule, the derivative of with respect to is .
Step 3.2.3
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.4
Add and .
Step 3.2.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.6
Differentiate using the Power Rule which states that is where .
Step 3.2.7
Multiply by .
Step 3.2.8
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.9
Differentiate using the Power Rule which states that is where .
Step 3.2.10
Multiply by .
Step 3.2.11
Differentiate using the Power Rule which states that is where .
Step 3.2.12
Simplify with factoring out.
Step 3.2.12.1
Multiply by .
Step 3.2.12.2
Factor out of .
Step 3.2.12.2.1
Factor out of .
Step 3.2.12.2.2
Factor out of .
Step 3.2.12.2.3
Factor out of .
Step 3.3
Cancel the common factors.
Step 3.3.1
Factor out of .
Step 3.3.2
Cancel the common factor.
Step 3.3.3
Rewrite the expression.
Step 3.4
Simplify.
Step 3.4.1
Apply the distributive property.
Step 3.4.2
Apply the distributive property.
Step 3.4.3
Simplify the numerator.
Step 3.4.3.1
Simplify each term.
Step 3.4.3.1.1
Move to the left of .
Step 3.4.3.1.2
Rewrite using the commutative property of multiplication.
Step 3.4.3.1.3
Multiply by by adding the exponents.
Step 3.4.3.1.3.1
Move .
Step 3.4.3.1.3.2
Multiply by .
Step 3.4.3.1.4
Multiply by .
Step 3.4.3.1.5
Multiply by .
Step 3.4.3.1.6
Multiply by .
Step 3.4.3.2
Combine the opposite terms in .
Step 3.4.3.2.1
Subtract from .
Step 3.4.3.2.2
Add and .
Step 3.4.3.3
Add and .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .