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

whose derivative is

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