Calculus Calculators

FreecalcHub offers the Derivative & Integral Calculator, which finds numerical derivatives at a point and definite integrals over an interval.

Type f(x) in the Derivative & Integral Calculator, choose derivative or definite integral, and give either the point to differentiate at or the two limits to integrate between. The answers are numerical: the derivative of x² at x = 3 comes back as 6, not as 2x, and an integral comes back as a number rather than an antiderivative.

Master derivatives and integrals as the core concepts of calculus.

No. The Derivative and Integral Calculator does not compute limits. It evaluates a derivative at a point and definite integrals numerically, and it refuses an integral whose function blows up inside the interval rather than attempting the limit; infinite limits of integration are not supported either.

Limits form the foundation for understanding derivatives and integrals.

Choose the definite integral mode, enter f(x) and the lower and upper limits, and the Derivative and Integral Calculator returns the signed area between the curve and the x-axis over that interval. Signed means area below the axis counts as negative. Volumes of revolution are not supported: set that integral up yourself and enter the resulting function.

Area calculations demonstrate the practical power of integral calculus.

That is what the derivative mode gives you: f′ at the point you name, which is both the instantaneous rate of change there and the slope of the tangent line at that point. Evaluate it at several points to see how the rate itself is changing.

Rate of change calculations are fundamental to understanding motion and growth.

There is no optimisation tool here: nothing solves f′(x) = 0 for you. What you can do is evaluate f′ at a series of points and watch for the sign change, which brackets a maximum or minimum, then narrow it down. Setting the problem up and solving for the critical point is the part you do yourself.

Not here. The Derivative and Integral Calculator takes one variable, x, so partial derivatives, multiple integrals and vector calculus are outside what it does. For an inner integral you have already reduced to a single variable, it will evaluate that.

The same two modes cover a great deal of it: the derivative at a point gives velocity from a position function or acceleration from a velocity function, and the definite integral gives displacement from velocity, or work from a force that varies. Trigonometric arguments can be read as degrees or radians.

Work the derivative or integral out by hand, then check the number. Evaluate your own answer at a point and compare it with what the calculator returns for the same point or interval. Agreement to several decimal places is strong evidence; a clean disagreement usually means a sign or a chain-rule slip.

Enough algebra to write the function correctly and enough trigonometry to know whether your angles are in degrees or radians. The Quadratic Equation Solver and the Scientific Calculator cover those two areas.

A calculus problem usually ends in ordinary algebra and arithmetic. The Quadratic Equation Solver finishes the quadratics, the Scientific Calculator evaluates expressions, the Geometry Calculator handles areas and volumes of standard shapes, and the Statistics Calculator handles data.