Symbolic Math Toolbox 

This example shows how to perform simple calculus operations using Symbolic Math Toolbox™.
To manipulate a symbolic variable, create an object of type SYM.
x = sym('x')
x = x
Once a symbolic variable is defined, you can use it to build functions. EZPLOT makes it easy to plot symbolic expressions.
f(x) = 1/(5+4*cos(x)) ezplot(f)
f(x) = 1/(4*cos(x) + 5)
Evaluate the function at x=pi/2 using math notation.
f(pi/2)
ans = 1/5
Many functions can work with symbolic variables. For example, DIFF differentiates a function.
f1 = diff(f) ezplot(f1)
f1(x) = (4*sin(x))/(4*cos(x) + 5)^2
DIFF can also find the Nth derivative. Here is the second derivative.
f2 = diff(f,2) ezplot(f2)
f2(x) = (4*cos(x))/(4*cos(x) + 5)^2 + (32*sin(x)^2)/(4*cos(x) + 5)^3
INT integrates functions of symbolic variables. The following is an attempt to retrieve the original function by integrating the second derivative twice.
g = int(int(f2)) ezplot(g)
g(x) = 8/(tan(x/2)^2 + 9)
At first glance, the plots for f and g look the same. Look carefully, however, at their formulas and their ranges on the yaxis.
subplot(1,2,1) ezplot(f) subplot(1,2,2) ezplot(g)
e is the difference between f and g. It has a complicated formula, but its graph looks like a constant.
e = f  g subplot(1,1,1) ezplot(e)
e(x) = 8/(tan(x/2)^2 + 9) + 1/(4*cos(x) + 5)
To show that the difference really is a constant, simplify the equation. This confirms that the difference between them really is a constant.
e = simplify(e) ezplot(e)
e(x) = 1