differentiate

Performs numerical differentiation at a point.

Syntax

• differentiate(expr, var, x[, ε])

  • expr is an expression in one variable var

  • var is the variable in expr

  • x is the point at which the derivative is computed

  • ε is the radius about x used for numerical differentiation

Description

differentiate computes a symmetric difference quotient for a real function of a real variable at a particular point in its domain:

differentiate(f(t), t, x, ε) = [f(t + ε) − f(t − ε)] / (2⋅ε).

If omitted, ε is set to 10^−6.

Examples

differentiate(x^2, x, 1)

2

differentiate(e^x, x, 1)

2.71828182846

∫(differentiate(x^2, x, t), t, 0, 2)

4

See also

• diff (synonym)

• ∫ (integrate)