Implicit Derivative Calculator

Implicit differentiation finds dy/dx for a curve given as an equation rather than as y written in terms of x. Enter an equation whose two sides are polynomials in x and y, such as x^2 + y^2 = 25, and the page moves everything to one side, takes both partial derivatives by the power rule and returns dy/dx as an exact quotient together with the second derivative. A second tab gives the slope, tangent line, normal line and concavity at a point, and rejects any point that does not satisfy the equation. Anything outside that grammar, such as a sine, a logarithm or a square root, is refused rather than approximated.