# Calculus Examples

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