Expressions and Derivative Rules for the Derivative Calculator


The expressions entered into the text field in the Derivative Calculator may include any combination of the following: These expressions are a subset of the expressions allowed in the other applets -- in particular, expressions in the Derivative Calculator do not include the functions int(...), max(...), or min(...), factorial expressions n!, or conditional expressions x?y:z. These restrictions are mostly intended to eliminate potential problems with derivatives at endpoints of intervals or jump discontinuities. However, since exponents are handled differently in this applet, the nrt(...) function is also not available (because it is unnecessary -- simply use fractional exponents).

Derivative Rules

In these rules, the derivative operator is D[...], u and v are expressions involving the free variable x, and c is a constant expression.

Partial Derivatives

The standard derivative operator D[...] represents a derivative with respect to the free variable x. This derivative operator can also be entered as Dx[...]. If other free variables appear in the expression, they are treated as constant (with respect to the free variable x), so that the derivative computed is actually a partial derivative with respect to x. Partial derivatives with respect to other available free variables can be computed by using the appropriate derivative operator: Dy[...] represents a partial derivative with respect to the free variable y, Dz[...] with respect to z, etc. Available free variables are: x, y, z, u, v, r, s, and t.


The following examples show partial derivatives of the same expression with respect to different variables.