Difference Quotient Calculator

Use ^ for powers and the usual function names: sin, cos, tan, ln, log, exp, sqrt, abs.
In partial-derivative mode the other variables are held constant.
The point a. In linearisation mode this is the centre of the approximation.
Used only to put a number to the symbolic difference quotient.
Derivative
2 * x + h
Derivative Calculator
Notation
[f(x + h) - f(x)] / h
Worked out from OpenStax, Calculus Volume 1, chapter 3 (Derivatives): the power, product, quotient and chain rules and 2 other sources.

How this is worked out

4 steps
  1. f(x + h) = (x + h)^2
  2. f(x + h) - f(x) = 2 * h * x + h^2
  3. Divide by h: 2 * x + h
  4. Letting h → 0 gives the derivative 2 * x.

Results are general information, not financial, tax, legal, medical or engineering advice.