# 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

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

Subtract from both sides of the equation.

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

Factor out of .

Step 5.2.3.1.2.2

Cancel the common factor.

Step 5.2.3.1.2.3

Rewrite the expression.

Step 5.2.3.2

Move the negative in front of the fraction.

Step 6

Replace with .