Calculus
Derivative Calculator
Estimate the slope of a function at a point using high-precision finite differences, with support for higher-order derivatives.
Evaluate first and higher-order derivatives numerically.
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
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Derivative Calculator: derivative calculator, first derivative calculator, higher order derivative calculator, derivative calculator with steps. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Derivative Calculator: Computes first through fourth derivatives at a point. It's built around derivative, differentiation, slope, so you can go from a raw question to a checked answer without switching tools.
The math behind it: Higher derivatives reuse the central-difference stencil recursively so you can inspect curvature and rate of change. The core relationship is f′(x₀) ≈ [f(x₀ + h) − f(x₀ − h)] / (2h), shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Enter the function f(x) you want to differentiate. (2) Provide the evaluation point x₀ and select the derivative order (1st–4th). (3) Review the resulting derivative value and slope approximation. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering f(x) = sin(x) * x^2 at x₀ = 1.2 returns f′(1.2) ≈ 1.5684. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
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.
What formula does the Derivative Calculator use?
Higher derivatives reuse the central-difference stencil recursively so you can inspect curvature and rate of change.
How do I use the Derivative Calculator?
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.