We've seen now that Matlab Function files can take arguments like myfunction$($a$,$b$)$ but what if we want to pass a symbolic Matlab function to myfunction? For example what if we want to write a function file which takes a function and a number, takes the derivative of the function and plugs in the number. Can we just do this?

function r $=$ myderivatpoint$($f$,$a$)$

syms x

r $=$ subs$($diff$($f$($x$)),$x$,$a$)$;

end

This is actually fine, except when we call the function we can't do this:

syms x

myderivatpoint$($x$^2+$x$+$sin$(5*$x$),17)$

The above code will return:

Error using sym$/$subsindex $($line $853)$

Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments must be symbolic variables, and

function body must be sym expression.

Error in sym$/$subsref $($line $898)$

R$\_$tilde $=$ builtin$(\text{'}$subsref$\text{'},$L$\_$tilde,Idx$)$;

Error in myfunction $($line $3)$

r $=$ subs$($diff$($f$($x$)),$x$,$a$)$;

Why not? The reason is that x$^2+$x$+$sin$(5*$x$)$ is interpreted as an expression, not a function, and so when we attempt to do f$($x$)$ inside of myfunction makes no sense. If we want to pass this expression we must pass it as something called a function handle, so the following will work. The @$($x$)$ tells Matlab that what follows is to be interpreted as a function with the variable x$,$ rather than an expression.

syms x

myderivatpoint$($@$($x$)$ x$^2+$x$+$sin$(5*$x$),17)$

This will yield the correct:

ans $=$

$5*$cos$(85)+35$

However if we've pre$-$defined a function ahead of time then we can pass it directly, because Matlab already knows it's a function, so this will work, too:

syms x

f$($x$)=$ x$^2+$x$+$sin$(5*$x$)$;

myderivatpoint$($f$,17)$

Yielding:

ans $=$

$5*$cos$(85)+35$

Assignment

Copy the above function code $($the first four code lines$)$ into the Function box and change it so it takes two functions f and g and one number a and so it finds the derivative of the composition $,$ plugs in $($read that carefully!$)$ and returns that value. Then submit it$.$