Derivatives · Basic Rules
Limit Definition of Derivative
The derivative of f at x is defined as the limit of the difference quotient as h approaches 0.
- 0 variables
- 2 worked examples
- 24 in Derivatives
Worked examples
Find f'(x) for f(x) = x² using the limit definition.
- f(x+h) = (x+h)² = x² + 2xh + h²
- [f(x+h) - f(x)]/h = (2xh + h²)/h = 2x + h
- lim(h→0) (2x + h) = 2x
Answer: f'(x) = 2x
1 more worked examplePremium
Find f'(x) for f(x) = 1/x using the limit definition.
Step-by-step solution locked.
Unlock the full working. CalcRef Premium opens the step-by-step solution above, and 141 worked solutions across the whole library - the intermediate lines, not just the answer. The formula statement, its conditions, its variables and the first worked example stay free on every page.
See all 24 Derivatives formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.
Practice
Quiz yourself on Derivatives
Limit Definition of Derivative is one of 24 Derivatives formulas in CalcRef, out of 136 in the library. Today's free round is 10 mixed multiple-choice questions drawn from the same dataset as this page, refreshed every day and replayable as often as you like - no account needed.