Does this derivative calculator show steps or a symbolic answer?

No. It is a numeric calculator that returns the value of the derivative at the single point you choose, computed by sampling the function with the central-difference method. It does not produce a symbolic formula or show algebraic steps.

Derivative Calculator — Numeric Slope f′(x)

Q: Which functions can I enter?

You can use + - * / and ^ plus sin, cos, tan, sqrt, exp, abs, and ln/log (both natural log), along with the constants pi and e. Always write the variable as x.

Q: Why do I get Invalid function or Undefined?

Invalid function means the expression contained characters or names the calculator does not recognize; check your syntax and that you used x. Undefined means the function or its slope is not finite at that point, such as log(x) at x = 0. Try a different point.

Direct answer: this tool evaluates the derivative (the instantaneous slope) of a function at a chosen value of x using high-accuracy numeric differentiation. It returns a numeric value at a single point — not a symbolic formula. Type a function of x and a point, and it computes f′(x) live as you type.

Evaluate a derivative

Function f(x)

Point x

Use x as the variable. Supports + − * / ^ and sin, cos, tan, sqrt, ln (use log for natural log), exp, pi.

How this calculator works

This is a numeric derivative calculator. Instead of finding a symbolic formula for f′(x), it estimates the slope of your function at one specific point using the central-difference method:

f′(x) ≈ ( f(x + h) − f(x − h) ) / (2h)

Here h is a tiny step (about 10⁻⁶, scaled with the size of x for accuracy). Because it samples the function just to the left and right of your point and measures how much the output changes, it returns the instantaneous slope — that is, the value of the derivative at that point. If the result is extremely close to a whole number, it is rounded for readability.

What you get is a single number, f′(x), for the x you entered. To see the derivative at a different point, just change the value of x and the answer updates instantly.

Differentiation rules

While this tool gives you a numeric answer, it helps to know the standard rules of differentiation so you can check results and understand the underlying calculus.

Power rule: if f(x) = xⁿ, then f′(x) = n·xⁿ⁻¹.
Product rule: (u·v)′ = u′v + uv′.
Quotient rule: (u/v)′ = (u′v − uv′) / v².
Chain rule: if y = f(g(x)), then y′ = f′(g(x))·g′(x).

Common derivatives reference

Function f(x)	Derivative f′(x)
c (constant)	0
xⁿ	n·xⁿ⁻¹
sin x	cos x
cos x	−sin x
tan x	sec² x
e^x	e^x
ln x	1 / x
√x	1 / (2√x)

Worked examples

f(x) = x² + 3x at x = 2. Symbolically f′(x) = 2x + 3, so f′(2) = 2(2) + 3 = 7. Enter x^2 + 3*x with x = 2 and the tool returns f′(2) ≈ 7.
f(x) = sin x at x = 0. Since the derivative of sin x is cos x, f′(0) = cos 0 = 1. Enter sin(x) with x = 0.
f(x) = e^x at x = 1. The derivative of e^x is e^x, so f′(1) = e ≈ 2.718. Enter exp(x) with x = 1.
f(x) = ln x at x = 2. The derivative of ln x is 1/x, so f′(2) = 1/2 = 0.5. Enter log(x) with x = 2 (remember log is the natural log here).

Frequently asked questions

Does this show steps or a symbolic answer?

No. This is a numeric calculator: it returns the value of the derivative at the single point you choose, computed by sampling the function. It does not produce a symbolic formula like f′(x) = 2x + 3 or show algebraic steps. Use the differentiation rules above to work out the symbolic form by hand.

How accurate is the result?

Central-difference differentiation is highly accurate for smooth functions — typically correct to several decimal places. Results that fall within 0.0001 of a whole number are rounded so you see clean values like 7 or 0.5.

Which functions can I use?

You can use + − * / ^ plus sin, cos, tan, sqrt, exp, abs, and ln/log (both natural log), along with the constants pi and e. Always write the variable as x.

Why do I get “Invalid function” or “Undefined”?

“Invalid function” means the expression contained characters or names the calculator does not recognize — check your syntax and that you used x. “Undefined” means the function or its slope is not finite at that point (for example, log(x) at x = 0). Try a different point.

Can it find the derivative at points where the function isn’t differentiable?

Numeric differentiation will still return a number near sharp corners or jumps (such as abs(x) at x = 0), but that value is not meaningful because the true derivative does not exist there. Treat results at non-smooth points with caution.

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Last reviewed: June 2026