Calculus
Derivative Calculator
Estimate the slope of a function at a point using high-precision finite differences, with support for higher-order derivatives.
derivativedifferentiationslope
Derivative Calculator
Evaluate first and higher-order derivatives numerically.
x₀
1.2
f'(x₀)
2.758689
Slope approximation
2.758689
Central difference
f′(x₀) ≈ [f(x₀ + h) − f(x₀ − h)] / (2h)
Higher derivatives reuse the central-difference stencil recursively so you can inspect curvature and rate of change.
How to use
- Enter the function f(x) you want to differentiate.
- Provide the evaluation point x₀ and select the derivative order (1st–4th).
- Review the resulting derivative value and slope approximation.
Example
Input: f(x) = sin(x) * x^2 at x₀ = 1.2
Output: f′(1.2) ≈ 1.5684
FAQ & notes
Can I change the step size?
The calculator internally uses a very small step (1e-5) suitable for most smooth functions. Rescale inputs if cancellation becomes an issue.
Does it return symbolic derivatives?
No—the result is numeric, which keeps the interface fast and flexible for arbitrary expressions.