# Calculus Examples

,
Step 1
Find the first derivative and evaluate at and to find the slope of the tangent line.
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
Step 1.4
Evaluate the derivative at .
Step 1.5
Simplify.
Step 1.5.1
Multiply by .
Step 1.5.2
Subtract from .
Step 2
Plug the slope and point values into the point-slope formula and solve for .
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