Computing Derivatives - Derive.nb

The Easy Way

There are two ways in which to compute the derivative. Let's start with the easier way: Define the function, let's say f(x), then evaluate f '(x).

When you define a function, it is essential to include the "_"-character on the left side of the definition; this is the signal for Mathematica to treat the "x" as a variable.

You can also compute higher derivatives this way:

The Alternative Way

This method uses the command "D" to compute derivatives.

You can indicate also that you want to find higher derivatives. Here is the third derivative of :

This works nicely for partial derivatives you encounter in Calculus III or Differential Equations. The next command evaluates the partial derivative of the function with respect to y:

Here is a mixed derivative

How do you evaluate the derivative at a point? (In the next command. read "/.{x->2}" as "afterwards replace x by 2")

A More Complicated Example

Let's create a list of the first 10 derivatives of the following function:

Here is the - for instance - the second derivative:

Here is the whole list, using the "Table" command. ("n" is a dummy variable, "{n,1,10,1}" means that n will take all values from 1 to 10, incrementing by 1.)

What about the derivatives evaluated at 0? Here we go:

0
0
12
0
0
1680
0