Calculus Examples
Step 1
Consider the limit definition of the derivative.
Step 2
Evaluate the function at .
Replace the variable with in the expression.
Simplify the result.
Apply the distributive property.
The final answer is .
Reorder and .
Find the components of the definition.
Step 3
Plug in the components.
Step 4
Simplify the numerator.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Multiply by .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Add and .
Subtract from .
Add and .
Multiply by .
Divide by .
Step 5
Evaluate the limit of which is constant as approaches .
Step 6