How to calculate gradients of a symbolic function

Hi,

I have a symbolic function of the form f = 2*y*z*sin(x) + 3*x*sin(z)*cos(y) and want to calcuate gradients with respect to x, y and z. I cannot define syms x y z before creating the function as its an input. Therefore, I defined syms x y z afterwards but its not working. The follwing error appeared:

Unable to convert expression into double array.

How do I calcuate gradients of this symbolic function?

Answer 1

[Walter Roberson]

%construct the input
syms x y z
f(x,y,z) = 2*y*z*sin(x) + 3*x*sin(z)*cos(y);
%and assume you are passing f into a different function so x y z are not still around

g = yadayada(f);

function g = yadayada(f)
  %so we have an input symbolic function but for some reason
  %we are not in the context where the variables came from. 
  %it turns out to be as simple as
  g = gradient(f);
  %or for greater certainty you could
  g = gradient(f, symvar(f));  %which is what the simple call does
  %or perhaps you have a reason to do
  syms x y z
  g = gradient(f(x, y, z), [x y z])
  %for example it might be a symbolic function in three other
  %variables that you want to re-label as x, y, z.
end

Answer 2

[Dirk]

How do I etermine the intervals on which a function is increasing and decreasing for x ϵ [0,4]

[Torsten]

syms x
f = x.*cos(x.^2)-exp(sqrt(x))+x.^3-4*x.^2;
df = diff(f,x);
f = matlabFunction(f);
df = matlabFunction(df);
x = 0:0.01:4;
plot(x,f(x))

x0 = [1.75 2.25];
sol(1) = fzero(df,x0);
x0 = [2.25 2.75];
sol(2) = fzero(df,x0);
x0 = [2.75 3.2];
sol(3) = fzero(df,x0);
x0 = [3.25 3.6];
sol(4) = fzero(df,x0);
x0 = [3.75 4];
sol(5) = fzero(df,x0);
sol

sol = 1×5

2.0016 2.4741 3.0614 3.5959 3.9127