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 other Mathlets -- 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.

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.