Question

If $z=e^{xy}$, then $dz$ is equal to

• A. $z(dx+dy)$
• B. $z(xdx+ydy)$
• C. $z(ydx+xdy)$
• D. $xdx+ydy$

Answer 1

The correct option is C

$z(ydx+xdy)$

The given information in the question is;

$z=e^{xy}$

Now we know since z is a function of x and y we have,

$dz=\frac{\partial z}{\partial x}dy+\frac{\partial z}{\partial y}dx$

Now we calculate the following,

$\Rightarrow \frac{\partial z}{\partial x}=y{e}^{xy}$

$\Rightarrow \frac{\partial z}{\partial x}=yz$

$\Rightarrow \frac{\partial z}{\partial y}=x{e}^{xy}$

$\Rightarrow \frac{\partial z}{\partial y}=xz$

So substituting these values in the equation we get,

$\Rightarrow dz=z(ydx+xdy)$