Answer
$\dfrac{1}{x \ln y}$ and $\dfrac{-\ln x}{y(\ln y)^2}$
Work Step by Step
We need to take the first partial derivatives of the given function.
In order to find the partial derivative, we will differentiate with respect to $x$, by keeping $y$ as a constant, and vice versa:
$f_x=\dfrac{1}{\ln y} \times \dfrac{\partial (\ln x)}{\partial x}=\dfrac{1}{x \ln y}$
$f_y=\ln (x) \times [(-\ln y)^2] \times \dfrac{\partial (\ln y)}{\partial y}=\dfrac{-\ln x}{y(\ln y)^2}$
