# Derivative (')

Derivative[n][f]
represents the nth derivative of the function f.
Derivative[n1, n2, ...][f]
represents a multivariate derivative.

• Derivative[1][Sin]

• Derivative[3][Sin]

• Derivative[2][# ^ 3&]

Derivative can be entered using ':

• Sin'[x]

• (# ^ 4&)''

• f'[x] // InputForm

• Derivative[1][#2 Sin[#1]+Cos[#2]&]

• Derivative[1,2][#2^3 Sin[#1]+Cos[#2]&]

Deriving with respect to an unknown parameter yields 0:

• Derivative[1,2,1][#2^3 Sin[#1]+Cos[#2]&]

The 0th derivative of any expression is the expression itself:

• Derivative[0,0,0][a+b+c]

You can calculate the derivative of custom functions:

• f[x_] := x ^ 2

• f'[x]

Unknown derivatives:

• Derivative[2, 1][h]

• Derivative[2, 0, 1, 0][h[g]]