Calculus Examples

Use the Limit Definition to Find the Derivative
Consider the limit definition of the derivative.
Find the components of the definition.
Tap for more steps...
Evaluate the function at .
Tap for more steps...
Replace the variable with in the expression.
Simplify the result.
Tap for more steps...
Simplify each term.
Tap for more steps...
Rewrite as .
Expand using the FOIL Method.
Tap for more steps...
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Tap for more steps...
Simplify each term.
Tap for more steps...
Multiply by .
Multiply by .
Add and .
Tap for more steps...
Reorder and .
Add and .
The final answer is .
Reorder.
Tap for more steps...
Move .
Reorder and .
Find the components of the definition.
Plug in the components.
Simplify.
Tap for more steps...
Simplify the numerator.
Tap for more steps...
Apply the distributive property.
Multiply by .
Subtract from .
Add and .
Add and .
Add and .
Factor out of .
Tap for more steps...
Factor out of .
Factor out of .
Factor out of .
Reduce the expression by cancelling the common factors.
Tap for more steps...
Cancel the common factor of .
Tap for more steps...
Cancel the common factor.
Divide by .
Reorder and .
Take the limit of each term.
Tap for more steps...
Split the limit using the Sum of Limits Rule on the limit as approaches .
Split the limit using the Product of Limits Rule on the limit as approaches .
Evaluate the limits by plugging in for all occurrences of .
Tap for more steps...
Evaluate the limit of which is constant as approaches .
Evaluate the limit of which is constant as approaches .
Evaluate the limit of by plugging in for .
Add and .
Enter YOUR Problem
Mathway requires javascript and a modern browser.
Cookies & Privacy
This website uses cookies to ensure you get the best experience on our website.
More Information