Answer
\begin{align*}
(a)&\frac{\partial f}{\partial x} = 6x+5y\\
(b)&\frac{\partial f}{\partial y} =5x+6y\\
(c)&\frac{\partial f}{\partial x}\bigg|_{y=7} = 6x+35\\
\end{align*}
Work Step by Step
Given $$f(x, y)=3 x^{2}+5 x y+2 y^{3}$$
Since
\begin{align*}
(a)&\frac{\partial f}{\partial x} = 6x+5y\\
(b)&\frac{\partial f}{\partial y} =5x+6y\\
(c)&\frac{\partial f}{\partial x}\bigg|_{y=7} = 6x+35\\
\end{align*}