Derivative Calculator — f′(x) at a Point (Numerical)
Quick answer: Select a function and enter x to compute f′(x) numerically using central difference approximation.
Calculate the derivative f′(x) of common functions at any x value using the central difference numerical method. Select from 8 common functions (x², x³, √x, sin, cos, ln, eˣ, 1/x) and enter the point to evaluate. Shows a table of f(x) and f′(x) values near your chosen x.
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Last reviewed: April 2026Report an error
Calculates f′(x) numerically using the central difference method.
f′(3)
6
f(x) = x². At x = 3: f(x) = 9, f′(x) ≈ 6.
Derivative Table near x = 3
| x=1 | x=1.5 | x=2 | x=2.5 | x=3 | x=3.5 | x=4 | x=4.5 | x=5 |
|---|---|---|---|---|---|---|---|---|
| 1 | 2.25 | 4 | 6.25 | 9 | 12.25 | 16 | 20.25 | 25 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Row 1: f(x) · Row 2: f′(x) | ||||||||
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How to Use This Derivative Calculator Calculator
- 1Select the function f(x) from the dropdown.
- 2Enter the x value to evaluate the derivative at.
- 3Read f(x), f′(x), and the derivative table.
Frequently Asked Questions
- The derivative f′(x) measures the instantaneous rate of change of f(x) at x. Geometrically, it is the slope of the tangent line to the curve at that point.
- f′(x) ≈ (f(x+h) − f(x−h)) / (2h) for a very small h. This gives a highly accurate numerical approximation of the derivative.
- f(x) = x² → f′(x) = 2x. At x=3: f′(3) = 6. This is the power rule: d/dx[xⁿ] = nxⁿ⁻¹.
- d/dx[sin(x)] = cos(x). At x=0: cos(0)=1. At x=π/2: cos(π/2)=0 (the sine curve is flat at its peak).
- Symbolic derivatives require a computer algebra system (CAS) that can parse expressions. Numerical methods give highly accurate answers for specific values without a CAS.
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