Derivative Calculator

Use our free derivative calculator to compute f'(x) and f''(x) at any point using numerical differentiation, or generate a table of derivative values across an interval.

Math

Mode

f(x) =

Point x

Start (table)

End (table)

Steps

Formula

Compute the derivative of any differentiable function at a point using the central difference method (2nd order accurate). Supports sin, cos, tan, exp, ln, sqrt, and polynomials.

f'(x) = lim(h→0) [f(x+h)−f(x−h)] / (2h)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter f(x) using x as variable.
2Supported: +, −, *, /, ^ (power), sin(), cos(), tan(), exp(), ln(), sqrt(), abs().
3Select first or second derivative, or generate a table.
4Enter the point x or range, then Calculate.

Examples

f(x)=x² at x=3

1.f'(x) = 2x
2.f'(3) = 6

Result: 6

f(x)=x² second derivative

1.f''(x) = 2 constant

Result: 2

Frequently Asked Questions

Numerically using central difference: f'(x) ≈ (f(x+h)−f(x−h))/(2h).

polynomials, sin, cos, tan, exp, ln, sqrt, abs — any expression using x.

Around h² ≈ 10⁻¹² accuracy for well-behaved functions (h=1e-6).

Yes, type 'pi' or use the symbol π.

Use the second derivative mode, or compute table values.

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CalculateMe Team

Last updated: 2026-07-14

Derivative Calculator

Formula

How It Works

Examples

f(x)=x² at x=3

f(x)=x² second derivative

Frequently Asked Questions

How is the derivative computed?

What functions are supported?

What is the error?

Can I use π?

What about higher derivatives?

Related Calculators

Derivative Calculator

Formula

How It Works

Examples

f(x)=x² at x=3

f(x)=x² second derivative

Frequently Asked Questions

How is the derivative computed?

What functions are supported?

What is the error?

Can I use π?

What about higher derivatives?

Related Calculators