yes if you don't know the function then you are correct....and if you know function is continuous then you can compute it different manner like if you take partial derivative first...
visit through this link
https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivatives/v/symmetry-of-second-partial-derivatives
If f is a continuous and differential function and second order partial derivatives of f is continuous then Fxy = Fyx. and u are right .
must visit through this link.
ht...