differentiate

Performs numerical differentiation at a point.

Syntax

differentiate(expr, var, x[, ε])
- expr is a real or complex, scalar-. vector-, or matrix-valued expression in var
- var, a symbol, is the variable in expr
- x is the real point at which the derivative is computed
- ε is the radius about x used for numerical differentiation

differentiate computes a symmetric difference quotient of an expression at a specified point:

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

If omitted, ε is set to 10^−6.

The expression may be real or complex, scalar-, vector-, or matrix-valued.

differentiate(x^2, x, 1)

differentiate(e^x, x, 1)

2.71828182846

∫(differentiate(x^2, x, t), t, 0, 2)

differentiate(❨cos(t), sin(t), t❩, t, π/6)

 ⎛     −0.5     ⎞
e⎜0.866025403784⎟
 ⎝      1       ⎠

differentiate(❨❨x, i⋅x❩, ❨−i⋅x, x❩❩, x, π)

⎛   1   1⋅i⎞
⎝−1⋅i     1⎠