# Calculus Examples

Differentiate both sides of the equation.

The derivative of with respect to is .

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 .

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

Add and .

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

Replace with .

Rewrite the equation as .

Subtract from both sides of the equation.

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 .

Simplify each term.

Apply the product rule to .

Raise to the power of .

Multiply by .

Apply the product rule to .

Raise to the power of .

Raise to the power of .

Simplify .

Multiply by .

Write as a fraction with denominator .

Multiply and .

Multiply by .

Move the negative in front of the fraction.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Multiply by .

Subtract from .

Move the negative in front of the fraction.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Multiply by .

Subtract from .

Move the negative in front of the fraction.

Find the points where .