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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
Subtract from .
Step 2.4
By the Sum Rule, the derivative of with respect to is .
Step 2.5
Differentiate using the chain rule, which states that is where and .
Step 2.5.1
To apply the Chain Rule, set as .
Step 2.5.2
Differentiate using the Power Rule which states that is where .
Step 2.5.3
Replace all occurrences of with .
Step 2.6
Rewrite as .
Step 2.7
Since is constant with respect to , the derivative of with respect to is .
Step 2.8
Rewrite as .
Step 2.9
Since is constant with respect to , the derivative of with respect to is .
Step 2.10
Add and .
Step 3
Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
By the Sum Rule, the derivative of with respect to is .
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Simplify the expression.
Step 3.5.1
Add and .
Step 3.5.2
Multiply by .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Step 5.1
Factor out of .
Step 5.1.1
Factor out of .
Step 5.1.2
Factor out of .
Step 5.1.3
Factor out of .
Step 5.2
Divide each term in by and simplify.
Step 5.2.1
Divide each term in by .
Step 5.2.2
Simplify the left side.
Step 5.2.2.1
Cancel the common factor of .
Step 5.2.2.1.1
Cancel the common factor.
Step 5.2.2.1.2
Rewrite the expression.
Step 5.2.2.2
Cancel the common factor of .
Step 5.2.2.2.1
Cancel the common factor.
Step 5.2.2.2.2
Divide by .
Step 5.2.3
Simplify the right side.
Step 5.2.3.1
Cancel the common factor of and .
Step 5.2.3.1.1
Factor out of .
Step 5.2.3.1.2
Cancel the common factors.
Step 5.2.3.1.2.1
Cancel the common factor.
Step 5.2.3.1.2.2
Rewrite the expression.
Step 6
Replace with .