Derivatives

The app differentiates by the rules – the sum, constant multiple, product, quotient and chain rules – and says at every step which rule it used. It also handles higher derivatives and the value of the derivative at a point. Basic functions (x², sin x, eˣ, …) can also be differentiated from the definition, as the limit of the difference quotient. The result comes with a graph of the function and its derivative.

For a function given implicitly by an equation in x and y (x³ + y³ = 3xy) it differentiates both sides by x (y as a function of x) and expresses y′, or uses the formula y′ = −F_x / F_y; it also finds y″ and, at a given point, the tangent and the normal, and draws the curve.

At a singular point (the curve crosses itself or has a cusp) it finds the tangents from the equation’s lowest-degree terms – for the folium at the origin x = 0 and y = 0.

How to enter it

`(x^2 sin x)'`	A derivative with a prime after the bracket.
`d/dx (e^x / x)`	The d/dx notation, also from a photo (\frac{d}{dx}).
`(x^3 ln x)''`	Higher derivatives with more primes, or with the order at the “Differentiate” chip.
`(x^2 + 1)'\|_{x=2}`	The derivative at a point, or fill in the point at the chip.
`x^2 sin x`	An expression with the “Differentiate” chip – there you also choose the order, the point and the method (by the rules / from the definition).
`x^3 + y^3 = 3xy`	An equation in x and y – the “Implicit derivative” chip (order 1 or 2, the method, a point [x₀; y₀]) or “Graph of the curve”; written diff(x^3+y^3=3xy, x).