Derivative Calculator

This derivative calculator differentiates a function of x and shows the result, then lets you evaluate that derivative at any point. The derivative is the central idea of differential calculus: it measures how quickly a function is changing, which is the slope of its graph at each point, and it is used everywhere from physics, where it turns position into velocity and velocity into acceleration, to economics, biology and engineering. You type a function using x as the variable, and the calculator applies the standard rules of differentiation, the power rule, the product and quotient rules and the chain rule, together with the known derivatives of sine, cosine, tangent, the exponential function, the natural logarithm and the square root. Enter the function with a star for multiplication, a caret for powers, and brackets around function arguments, so a cubic is written 3*x^2 + 2*x and a composite is written something like sin(2*x) or exp(x^2); note that implicit multiplication such as 2x is not read, so always write 2*x. The calculator returns the derivative as an expression, and if you enter a value it also gives the numeric slope at that point, which is handy for finding gradients, rates of change and stationary points. Enter a function to see its derivative straight away.

Use * for multiply and ^ for powers. Functions: sin, cos, tan, asin, acos, atan, exp, ln, log, sqrt, abs. Estimate only.