About this tool
The Derivative Calculator is a free, in-browser calculus tool that finds the exact symbolic derivative d/dx of a function you type in the variable x. It parses your expression into an expression tree and differentiates it with the standard rules of calculus: the sum and difference rules, the product rule (uv)' = u'v + uv', the quotient rule (u/v)' = (u'v − uv')/v², the power rule d/dx xⁿ = n·xⁿ⁻¹, and the chain rule for composed functions f(g(x))' = f'(g)·g'. It knows the derivatives of sin, cos, tan, sec, csc, cot, the inverse trig functions, exp, ln, log, sqrt, the hyperbolic functions, and more.
Everything runs locally in your browser with plain JavaScript, so nothing you type is uploaded or stored. After differentiating, the tool algebraically simplifies the result — folding constants, dropping ×1 and +0, and collapsing trivial powers — so the derivative comes back in a clean, readable form. You can use +, −, ×, ÷, ^ for powers, parentheses, and the constants pi and e, and implicit multiplication like 2x or 3sin(x) is understood.
Enter an optional evaluation point and the calculator also reports f(a) and f'(a), the slope of the tangent line at x = a. For example, the derivative of x³ + 2x is 3x² + 2, which equals 14 at x = 2. This mirrors the derivative pages of Symbolab and Wolfram Alpha while working entirely offline in your browser.