Question

For the two functions

$f(x,y)=x^3$-$3x{y}^2$ and $g(x,y)=3x^{2}y$ -$y^2$

Which one of the following options is correct?

• A. $\frac{\partial f}{\partial x}=\frac{\partial g}{\partial x}$
• B. $\frac{\partial f}{\partial x}=-\frac{\partial g}{\partial x}$
• C. $\frac{\partial f}{\partial y}=-\frac{\partial g}{\partial x}$
• D. $\frac{\partial f}{\partial y}=\frac{\partial g}{\partial x}$

Answer 1

The correct option is C $\frac{\partial f}{\partial y}=-\frac{\partial g}{\partial x}$

$\frac{\partial f}{\partial x}=3x^2-3y^2,\frac{\partial f}{\partial y}=-6xy$

$\frac{\partial g}{\partial x}=6xy,\frac{\partial g}{\partial y}=3x^2-3y^2$

So, $\frac{\partial f}{\partial y}=\frac{\partial g}{\partial x}$