Beyond the Basics - A Guide to MATLAB for Beginners and Experienced Users - page 61

Doing Calculus with MATLAB
MATLAB has commands for most of the computations of basic calculus
initsSymbolicMathToolbox.Thistoolboxincludespartofaseparateprogram
called Maple , which processes the symbolic calculations.
Differentiation
You can use diff to differentiate symbolic expressions, and also to approxi-
mate the derivative of a function given numerically (say by an M-file):
>> syms x; diff(xˆ3)
ans =
3*x^2
Here MATLAB has figured out that the variable is x . (See Default Variables
at the end of the chapter.) Alternatively,
>> f = inline('xˆ3', 'x'); diff(f(x))
ans =
3*x^2
The syntax for second derivatives is diff(f(x), 2) , and for n thderivatives,
diff(f(x), n) . The command diff can also compute partial derivatives
of expressions involving several variables, as in diff(xˆ2*y, y) , but to do
multiple partials withrespect to mixed variables you must use diff repeat-
edly, as in diff(diff(sin(x*y/z), x), y) . (Remember to declare y and
z symbolic.)
There is one instance where differentiation must be represented by the
letter D , namely when you need to specify a differential equation as input to
a command. For example, to use the symbolic ODE solver on the differential
equation xy + 1 = y , you enter
dsolve('x*Dy + 1 = y', 'x')