Originally Posted by

**el123** Says $\displaystyle f_{xy}=f_{yx}$

The original equation is

$\displaystyle f(x,y)=x^3\ln(1-xy)$

So for the first derivative with respect to x ,I used the product rule on first part then the quotient rule on second part to get the derivative below.

$\displaystyle f_x= 3x^2\ln(1-xy)-\frac{x^3y}{1-xy}$ Correct

Then for this one I just had to differentiate with respect to y which made it this.

$\displaystyle f_y=\frac{x^4}{1-xy}$ Correct if you make it negative

However i want to find $\displaystyle f_{xy}$

But i dont quite understand what it means , and the answers i get do not match each other according to youngs theorum.

Any suggestions?

Youngs theorum = $\displaystyle f_{xy}=f_{yx}$