# Calculus Examples

Step 1

Differentiate both sides of the equation.

Step 2

Step 2.1

Differentiate.

Step 2.1.1

By the Sum Rule, the derivative of with respect to is .

Step 2.1.2

Differentiate using the Power Rule which states that is where .

Step 2.2

Evaluate .

Step 2.2.1

Differentiate using the chain rule, which states that is where and .

Step 2.2.1.1

To apply the Chain Rule, set as .

Step 2.2.1.2

Differentiate using the Power Rule which states that is where .

Step 2.2.1.3

Replace all occurrences of with .

Step 2.2.2

Rewrite as .

Step 3

Step 3.1

Since is constant with respect to , the derivative of with respect to is .

Step 3.2

Differentiate using the Product Rule which states that is where and .

Step 3.3

Rewrite as .

Step 3.4

Differentiate using the Power Rule which states that is where .

Step 3.5

Multiply by .

Step 3.6

Apply the distributive property.

Step 4

Reform the equation by setting the left side equal to the right side.

Step 5

Step 5.1

Subtract from both sides of the equation.

Step 5.2

Subtract from both sides of the equation.

Step 5.3

Factor out of .

Step 5.3.1

Factor out of .

Step 5.3.2

Factor out of .

Step 5.3.3

Factor out of .

Step 5.4

Divide each term in by and simplify.

Step 5.4.1

Divide each term in by .

Step 5.4.2

Simplify the left side.

Step 5.4.2.1

Cancel the common factor of .

Step 5.4.2.1.1

Cancel the common factor.

Step 5.4.2.1.2

Rewrite the expression.

Step 5.4.2.2

Cancel the common factor of .

Step 5.4.2.2.1

Cancel the common factor.

Step 5.4.2.2.2

Divide by .

Step 5.4.3

Simplify the right side.

Step 5.4.3.1

Simplify each term.

Step 5.4.3.1.1

Cancel the common factor of .

Step 5.4.3.1.1.1

Cancel the common factor.

Step 5.4.3.1.1.2

Rewrite the expression.

Step 5.4.3.1.2

Cancel the common factor of and .

Step 5.4.3.1.2.1

Factor out of .

Step 5.4.3.1.2.2

Cancel the common factors.

Step 5.4.3.1.2.2.1

Cancel the common factor.

Step 5.4.3.1.2.2.2

Rewrite the expression.

Step 5.4.3.1.3

Move the negative in front of the fraction.

Step 5.4.3.2

Combine the numerators over the common denominator.

Step 6

Replace with .