# Calculus Examples

,

Step 1

Step 1.1

Differentiate.

Step 1.1.1

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

Step 1.1.2

Differentiate using the Power Rule which states that is where .

Step 1.2

Evaluate .

Step 1.2.1

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

Step 1.2.2

Differentiate using the Power Rule which states that is where .

Step 1.2.3

Multiply by .

Step 1.3

Differentiate using the Constant Rule.

Step 1.3.1

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

Step 1.3.2

Add and .

Step 1.4

Evaluate the derivative at .

Step 1.5

Simplify.

Step 1.5.1

Multiply by .

Step 1.5.2

Add and .

Step 2

Step 2.1

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

Step 2.2

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

Step 2.3

Solve for .

Step 2.3.1

Simplify .

Step 2.3.1.1

Rewrite.

Step 2.3.1.2

Simplify by adding zeros.

Step 2.3.1.3

Apply the distributive property.

Step 2.3.1.4

Multiply by .

Step 2.3.2

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

Step 2.3.2.1

Add to both sides of the equation.

Step 2.3.2.2

Add and .

Step 3