# Calculus Examples

,

Simplify .

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Remove parentheses.

Simplify and combine like terms.

Simplify each term.

Multiply by by adding the exponents.

Combine and

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Move to the left of the expression .

Multiply by .

Multiply by .

Add and .

Differentiate both sides of the equation.

The derivative of with respect to is .

Differentiate the right side of the equation.

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 .

Evaluate at .

Replace the variable with in the expression.

Multiply by .

Add and .

Plug in the slope of the tangent line and the and values of the point into the point-slope formula .

The slope-intercept form is , where is the slope and is the y-intercept.

Rewrite in slope-intercept form.

Simplify .

Simplify the expression.

Multiply by .

Multiply by .

Apply the distributive property.

Multiply by .

Multiply by .

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

Add to both sides of the equation.

Add and .