# Calculus Examples

Differentiate both sides of the equation.

The derivative of with respect to is .

Differentiate.

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

Differentiate using the Power Rule which states that is where .

Evaluate .

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

Differentiate using the Power Rule which states that is where .

Multiply by .

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

Replace with .

Factor the left side of the equation.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Rewrite as .

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Remove unnecessary parentheses.

Divide each term by and simplify.

Divide each term in by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by .

Divide by .

Set equal to and solve for .

Set the factor equal to .

Subtract from both sides of the equation.

Set equal to and solve for .

Set the factor equal to .

Add to both sides of the equation.

The solution is the result of and .

Simplify each term.

Raising to any positive power yields .

Raising to any positive power yields .

Multiply by .

Add and .

Simplify each term.

Raise to the power of .

Raise to the power of .

Multiply by .

Subtract from .

Find the points where .