Calculus Examples
,
Step 1
Step 1.1
Rewrite as .
Step 1.2
Expand using the FOIL Method.
Step 1.2.1
Apply the distributive property.
Step 1.2.2
Apply the distributive property.
Step 1.2.3
Apply the distributive property.
Step 1.3
Simplify and combine like terms.
Step 1.3.1
Simplify each term.
Step 1.3.1.1
Multiply by .
Step 1.3.1.2
Move to the left of .
Step 1.3.1.3
Multiply by .
Step 1.3.2
Add and .
Step 1.4
By the Sum Rule, the derivative of with respect to is .
Step 1.5
Differentiate using the Power Rule which states that is where .
Step 1.6
Since is constant with respect to , the derivative of with respect to is .
Step 1.7
Differentiate using the Power Rule which states that is where .
Step 1.8
Multiply by .
Step 1.9
Since is constant with respect to , the derivative of with respect to is .
Step 1.10
Add and .
Step 1.11
Evaluate the derivative at .
Step 1.12
Simplify.
Step 1.12.1
Multiply by .
Step 1.12.2
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