Derivative Calculator

The Derivative Calculator differentiates any expression you give it and labels each step with the rule applied. Power rule, product rule, quotient rule, chain rule, and the derivatives of exponential, logarithmic, trigonometric, inverse trigonometric and hyperbolic functions. It handles implicit differentiation for relations like x^3 + y^3 = 6xy, logarithmic differentiation for products of powers, second and higher derivatives, and evaluation at a point for a tangent line or an instantaneous rate. Partial derivatives of multivariable functions are supported when you state the variable. Piecewise functions, functions with absolute values, and inverse functions are handled with the relevant case or theorem stated before differentiation.

Type the function or photograph it. Say what to differentiate with respect to if it is not x: "d/dt of ..." or "dy/dx for ...". Ask for the second derivative, or the derivative at x = 2, or the tangent line at a point, in the same line. Use standard notation: sin(3x), e^(2x), ln(x), x^(1/2). Set Answer form to exact for symbolic results and decimal when you want a rounded value at a point. For related-rates or optimisation problems, paste the whole problem; the solver writes the relation, differentiates it, and substitutes the given rates or solves for the extremum, with each part labeled. For a partial derivative, say "partial with respect to y" and the other variables are held constant.

The output leads with the derivative in simplified form, then the step chain: identify the outer and inner functions, apply the rule, differentiate each piece, combine, simplify. Implicit problems show the y' terms collected on one side before solving. The working is shown so you can check it. For the antiderivative, use the Integral Calculator. To find critical points, intervals of increase, and concavity from the derivative, use the Function Analyzer. A follow-up can rerun the derivative using the limit definition when the course requires it, or evaluate the second derivative at a point for concavity. Every rule application is a line you can match to a table of derivative rules.