# Matlab – Symbolic & Function Handles

Standard

Consider you want to define a function in Matlab, plot it, and differentiate it. This can be done in two ways. Let’s demonstrate the two methods on the function $f(x) = x - 3 * log(x)$

whose derivative is $f'(x) = 1 - \frac{3}{x}$

The first is using function handles (ie; numerically) that take & return values as input & output. Function handles require the inputs to be initialized. Here’s an example:


x = linspace(0.5, 5.0)'; % range of x as column vector
f = x - 3 * log(x); % returns numerical values
df = diff(f) ./ diff(x); % also numerical values of the derivative



The other is symbolically (ie; like you do in your math class) as such


syms x % define symbolic variables
f = x - 3 * log(x); % symbolic function
df = diff(f, x); % gives the symbolic derivative



which returns

f = x - 3*log(x)
df = 1 - 3/x



But this way you cannot give the funtion numerical inputs and hence can’t plot it. To do so you’ll have to convert the function to a function handle which is easy using matlabFunction():


f_handle = matlabFunction(f); % convert symbolic fn to a handle
f_handle(2); % value of f @ x = 2
x = linspace(0.5, 5.0)'; % define range for x as column vector
plot(x, f_handle(x) ) % plot f on the range x



which return

f_handle = @(x)x-log(x).*3.0
df_handle = @(x)-3.0./x+1.0