evaluate jacobian using fsolve

my function and corresponding jacobian are:

function [F,J] = myfun(x)
    global m mxm Dvec gamma_0 tau_0
    Ft = zeros(5,5);
    n = 5;
    for ki = 1:12
        Fi = ((abs(m(ki,:)*x)/tau_0)^(n-1))*mxm(:,:,ki);
        Ft = Ft+Fi;
    end
    F = (gamma_0/tau_0)*Ft*x-Dvec;
    J = n*(gamma_0/tau_0)*Ft;
end

in which m is a 5x1x12 vector list, mxm is a 5x5x12 matrix list, input x is a 5x1 vector. the returned function F is a 5x1 vector and J is the 5x5 jacobian of F.

Interestingly, when I use fsolve to evaluate the function, I can get the desired results. However, when I increase the exponent,n, to larger than 5, the fsolve returns the DerivativeCheck fail information: Maximum relative difference between supplied and finite-difference derivatives = 0.0115267.

I wonder how matlab handle this evaluation. Is there a way to write the jacobian more effectively for a function like this?

thank you,