Approximating derivatives

The nDeriv command numerically approximates the value of a derivative.

nDeriv takes as arguments:
- expr, expression.
- Optionally, x, the variable used in the expression (by default x).
- Optionally, h (by default 0.001).
nDeriv(ex ⟨,x,h ⟩) returns an approximated value of the derivative of the expression ex at the point x using the formula:

f(x+h)−f(x−h)

2h

For a more general command on numeric differentiation, see Section 13.2.4.

nDeriv(x^2,x)

⎛
⎝

x+0.001

⎞
⎠

²−

⎛
⎝

x−0.001

⎞
⎠

· 500.0

subst(nDeriv(x^2,x),x=1)

2.0

nDeriv(exp(x^2),x,0.00001)

⎛
⎜
⎝

⎛
⎝

x+1.0×10⁻⁵

⎞
⎠

−e

⎛
⎝

x−1.0×10⁻⁵

⎞
⎠

⎞
⎟
⎠

· 50000.0

subst(exp(nDeriv(x^2,x,0.00001)),x=1)

7.38905609706

which is an approximate value of e²≈ 7.38905609893.