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• → DiscreteLimit

Derivative (')

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f'[x,...]

represents the derivative of f with respect to the first argument x.

f''[x,...]

represents the 2nd derivative of f with respect to x.

Derivative[n][f]

represents the nth derivative of the function f.

Derivative[$n_1$, $n_2$, ...][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]]