How to | Take a Derivative
The Wolfram Language makes it easy to take even the most complicated derivatives involving any of its huge range of differentiable special functions.
Define a function with one variable, :

https://wolfram.com/xid/0czd19yvhqrl1bnj93rw6he-nyxrnp

To find , type f'[x] and press
:

https://wolfram.com/xid/0czd19yvhqrl1bnj93rw6he-g3cx29

This method works for any order; just add more primes:

https://wolfram.com/xid/0czd19yvhqrl1bnj93rw6he-xemwab

Or use D. Its first argument is the function and its second argument is the variable:

https://wolfram.com/xid/0czd19yvhqrl1bnj93rw6he-ft068f

For higher-order derivatives using D, the second argument is a list, {variable,order}:

https://wolfram.com/xid/0czd19yvhqrl1bnj93rw6he-irdx5k

Define a function with two variables, :

https://wolfram.com/xid/0czd19yvhqrl1bnj93rw6he-e51vlt

Take the first derivative with respect to and the second with respect to
by combining the two forms (single variable and list):

https://wolfram.com/xid/0czd19yvhqrl1bnj93rw6he-jvgvj0

The Heaviside theta function is treated as if it had an infinite pulse at zero, where it is undefined:

https://wolfram.com/xid/0czd19yvhqrl1bnj93rw6he-brsanq

The HeavisideTheta function has special derivative properties:

https://wolfram.com/xid/0czd19yvhqrl1bnj93rw6he-6tlrvy

This plots the HeavisideTheta (green) and DiracDelta (red) functions:

https://wolfram.com/xid/0czd19yvhqrl1bnj93rw6he-bnnct
