How to use clairaut's theorem with 3rd order partial derivatives

[physicsidiot1]

Homework Statement

Use Clairaut's Theorem to show that is the third order partial derivatives are continuous, then f_xxy=f_yxy=f_yyz

Clairaut's Theorem being: f_xy(a,b)=f_yx(a.b)

Homework Equations

f_xyy=d/dy(d²f/dydx)=d^3f/dy^2dx

The Attempt at a Solution

Tried to differentiate the second partial derivatives but it didn't work out.

 

[pro_solver]

counter example

Try when f = (x^3)(y^2)(z). After differentiating, try (5,7,11).