# Calculus Examples

,

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Move to the left of .

Multiply by .

Add and .

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

Differentiate using the Power Rule which states that is where .

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 .

Evaluate the derivative at .

Simplify.

Multiply by .

Add and .

Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .

Simplify the equation and keep it in point-slope form.

Solve for .

Simplify .

Apply the distributive property.

Multiply by .

Move all terms not containing to the right side of the equation.

Add to both sides of the equation.

Add and .