• ← Complexes
• → Derivative

D

Derivative (WMA)

D[f, x]

gives the partial derivative of f with respect to x.

D[f, x, y, ...]

differentiates successively with respect to x, y, etc.

D[f, {x, n}]

gives the multiple derivative of order n.

D[f, {{$x_1$, $x_2$, ...}}]

gives the vector derivative of f with respect to $x_1$, $x_2$, etc.

First-order derivative of a polynomial:

• • D[x^3 + x^2, x]

Second-order derivative:

• • D[x^3 + x^2, {x, 2}]

Trigonometric derivatives:

• • D[Sin[Cos[x]], x]

• • D[Sin[x], {x, 2}]

• • D[Cos[t], {t, 2}]

Unknown variables are treated as constant:

• • D[y, x]

• • D[x, x]

• • D[x + y, x]

Derivatives of unknown functions are represented using Derivative:

• • D[f[x], x]

• • D[f[x, x], x]

• • D[f[x, x], x] // InputForm

Chain rule:

• • D[f[2x+1, 2y, x+y], x]

• • D[f[x^2, x, 2y], {x,2}, y] // Expand

Compute the gradient vector of a function:

• • D[x ^ 3 * Cos[y], {{x, y}}]

Hesse matrix:

• • D[Sin[x] * Cos[y], {{x,y}, 2}]