Derivative Calculator

Need a derivative, fast? Hand us your function and we'll differentiate it (and tidy up the result).

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Evaluate at x =

What this derivative calculator does

Give it a function of x and it returns the symbolic derivative — the exact formula for the slope, not just a number. It handles polynomials, roots, exponentials, logs, and the trig functions, applying the chain rule, product rule, and quotient rule for you, then simplifying the result. For example, the derivative of x² is 2x, the derivative of sin(x) is cos(x), and the derivative of x·e^x is e^x(x + 1).

When you'd reach for it

It's handy for checking calculus homework before you turn it in, finding the slope of a curve at a specific point, or locating maxima and minima by seeing where the derivative equals zero. Engineers and students use it to sanity-check hand work, and if you optionally evaluate the derivative at a point — say x = 2 — you get the instantaneous rate of change there, which is the slope of the tangent line at that spot.

Writing your function so it parses

A few formatting notes save headaches. Use ^ for powers (write x^3, not x³) and always include the multiplication sign: 3*x, not 3x. Wrap function arguments in parentheses, like sin(x) or ln(x). Use sqrt(x) for square roots and e^x or exp(x) for the exponential. A common gotcha is unbalanced parentheses in nested expressions — count your opening and closing brackets if you get an error.

How to use it

Type your function of x into the input box, for example x^3 - 5*x + 2.
Press calculate to see the simplified symbolic derivative.
Optionally enter an x-value to evaluate the derivative at that point and get the numeric slope.
Copy the result, or tweak the function and recalculate as many times as you like.

FAQ

Does it show higher-order derivatives?: Feed the first derivative back in as your new function to get the second derivative, then repeat for the third, and so on.
Why does my answer look different from my textbook's?: Both can be correct — derivatives can be written in several equivalent forms. Try evaluating both at a point; if they match, they're the same.
Can it handle variables other than x?: This tool differentiates with respect to x, so write your function using x as the variable.
Is it free, and does my function leave my device?: It's free and ad-supported, and the math runs entirely in your browser — nothing you type is uploaded.