Answer
\begin{align*}
(a)&\frac{\partial k}{\partial x} =\frac{x}{ x+y}+\ln (x+y) \\
(b)&\frac{\partial k}{\partial y} =\frac{x}{ x+y}\\
(c)&\frac{\partial k}{\partial y}\bigg|_{x=3} = \frac{3}{ 3+y}\\
(d)&\frac{\partial k}{\partial y}\bigg|_{(3,2)} = \frac{5}{ 5}\\
\end{align*}
Work Step by Step
Given $$k(x, y)=x \ln (x+y)
$$
Since
\begin{align*}
(a)&\frac{\partial k}{\partial x} =\frac{x}{ x+y}+\ln (x+y) \\
(b)&\frac{\partial k}{\partial y} =\frac{x}{ x+y}\\
(c)&\frac{\partial k}{\partial y}\bigg|_{x=3} = \frac{3}{ 3+y}\\
(d)&\frac{\partial k}{\partial y}\bigg|_{(3,2)} = \frac{5}{ 5}\\
\end{align*}
