Calculate the derivative f'(x) of a function at a specific x value. Enter standard mathematical expressions such as x^2 + 2x, 3x^2 - 4x + 1, 2(x+1), or sin(x).
Enter a function of x and the point where you want to calculate its derivative. The calculator uses numerical differentiation.
This calculator accepts common mathematical notation with implicit multiplication. You do not need to write an asterisk between a coefficient and x.
3x^2.
The derivative of a function measures its instantaneous rate of change. For a function f(x), the derivative is written as f'(x).
When the derivative is evaluated at a particular value x = a, it gives the instantaneous slope of the function at that point.
Geometrically, the derivative at a point is the slope of the tangent line to the function at that point.
This page calculates the derivative numerically rather than symbolically. It uses a central-difference approximation.
A small value of h is used to estimate the slope from function values immediately to the left and right of the selected point.
Enter:
Then choose an x value such as:
Derivatives are used throughout mathematics, science, engineering, economics and data analysis to describe rates of change.
For more advanced problems, you can also use the Critical Point Calculator or Higher-Order Derivative Calculator .
Summe.org provides several derivative and calculus tools for different types of problems.
When a function contains multiple variables, Summe.org also provides tools for gradients, directional derivatives and other multivariable calculus operations.
Derivatives and integrals are two fundamental operations in calculus. Differentiation studies rates of change, while integration studies accumulation and area.
The Fundamental Theorem of Calculus establishes an important connection between these operations.
Yes. The calculator automatically interprets
2x as 2*x. Therefore,
both x^2 + 2x and
x^2 + 2*x are accepted.
Yes. The calculator recognizes the implicit multiplication
between 3 and x, so 3x^2 is accepted.
Yes. The calculator converts the implicit multiplication into
the equivalent expression 2*(x+1).
Yes. Expressions such as x(x+1) are supported.
The derivative at a point represents the instantaneous rate of change of the function and, geometrically, the slope of its tangent line at that point.
No. This particular tool calculates the derivative numerically at a selected point. If you need the symbolic derivative of an entire function, use the Derivative Calculator .
The calculator uses a central-difference approximation: [f(x+h) − f(x−h)] / (2h), with a small numerical step size.
Yes. Enter sin(x) and specify the x value where
you want the numerical derivative.
The calculator will return an error if the function cannot be evaluated at the selected point or at one of the nearby points used for the numerical approximation.
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