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Calculus Examples
Step 1
Differentiate both sides of the equation.
Step 2
Step 2.1
Rewrite as .
Step 2.2
Expand using the FOIL Method.
Step 2.2.1
Apply the distributive property.
Step 2.2.2
Apply the distributive property.
Step 2.2.3
Apply the distributive property.
Step 2.3
Simplify and combine like terms.
Step 2.3.1
Simplify each term.
Step 2.3.1.1
Multiply by .
Step 2.3.1.2
Move to the left of .
Step 2.3.1.3
Multiply by .
Step 2.3.2
Add and .
Step 2.4
Rewrite as .
Step 2.5
Expand using the FOIL Method.
Step 2.5.1
Apply the distributive property.
Step 2.5.2
Apply the distributive property.
Step 2.5.3
Apply the distributive property.
Step 2.6
Simplify and combine like terms.
Step 2.6.1
Simplify each term.
Step 2.6.1.1
Multiply by .
Step 2.6.1.2
Move to the left of .
Step 2.6.1.3
Multiply by .
Step 2.6.2
Subtract from .
Step 2.7
Differentiate.
Step 2.7.1
By the Sum Rule, the derivative of with respect to is .
Step 2.7.2
Differentiate using the Power Rule which states that is where .
Step 2.8
Evaluate .
Step 2.8.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.8.2
Differentiate using the Power Rule which states that is where .
Step 2.8.3
Multiply by .
Step 2.9
Since is constant with respect to , the derivative of with respect to is .
Step 2.10
Evaluate .
Step 2.10.1
Differentiate using the chain rule, which states that is where and .
Step 2.10.1.1
To apply the Chain Rule, set as .
Step 2.10.1.2
Differentiate using the Power Rule which states that is where .
Step 2.10.1.3
Replace all occurrences of with .
Step 2.10.2
Rewrite as .
Step 2.11
Evaluate .
Step 2.11.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.11.2
Rewrite as .
Step 2.12
Since is constant with respect to , the derivative of with respect to is .
Step 2.13
Simplify.
Step 2.13.1
Combine terms.
Step 2.13.1.1
Add and .
Step 2.13.1.2
Add and .
Step 2.13.2
Reorder terms.
Step 3
Since is constant with respect to , the derivative of with respect to is .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Step 5.1
Move all terms not containing to the right side of the equation.
Step 5.1.1
Subtract from both sides of the equation.
Step 5.1.2
Subtract from both sides of the equation.
Step 5.2
Factor out of .
Step 5.2.1
Factor out of .
Step 5.2.2
Factor out of .
Step 5.2.3
Factor out of .
Step 5.3
Divide each term in by and simplify.
Step 5.3.1
Divide each term in by .
Step 5.3.2
Simplify the left side.
Step 5.3.2.1
Cancel the common factor of .
Step 5.3.2.1.1
Cancel the common factor.
Step 5.3.2.1.2
Rewrite the expression.
Step 5.3.2.2
Cancel the common factor of .
Step 5.3.2.2.1
Cancel the common factor.
Step 5.3.2.2.2
Divide by .
Step 5.3.3
Simplify the right side.
Step 5.3.3.1
Simplify each term.
Step 5.3.3.1.1
Cancel the common factor of and .
Step 5.3.3.1.1.1
Factor out of .
Step 5.3.3.1.1.2
Cancel the common factors.
Step 5.3.3.1.1.2.1
Cancel the common factor.
Step 5.3.3.1.1.2.2
Rewrite the expression.
Step 5.3.3.1.2
Move the negative in front of the fraction.
Step 5.3.3.1.3
Cancel the common factor of and .
Step 5.3.3.1.3.1
Factor out of .
Step 5.3.3.1.3.2
Cancel the common factors.
Step 5.3.3.1.3.2.1
Cancel the common factor.
Step 5.3.3.1.3.2.2
Rewrite the expression.
Step 5.3.3.1.4
Move the negative in front of the fraction.
Step 5.3.3.2
Simplify terms.
Step 5.3.3.2.1
Combine the numerators over the common denominator.
Step 5.3.3.2.2
Factor out of .
Step 5.3.3.2.3
Rewrite as .
Step 5.3.3.2.4
Factor out of .
Step 5.3.3.2.5
Simplify the expression.
Step 5.3.3.2.5.1
Rewrite as .
Step 5.3.3.2.5.2
Move the negative in front of the fraction.
Step 6
Replace with .