Assign value to symbolic function?

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I have a symbolic function $g(x,y)$, which depends on the variables $x$ and $y$. Using this, I define the function $f(x,y)$ as: \begin{equation} f(x,y) = g(x,y) + 2x. \end{equation}

If I calculate the derivative of $f(x,y)$ with respect to $x$: \begin{equation} \frac{df(x,y)}{dx}=\frac{dg(x,y)}{dx}+2. \end{equation}

Now, I need to evaluate this at $x=0$, knowing that $\frac{dg(x,y)}{dx}\bigg\rvert_{x=0}=10$. This should give me: \begin{equation} \frac{df(x,y)}{dx}\bigg\rvert_{x = 0} = \frac{dg(x,y)}{dx}\bigg\rvert_{x = 0} +2=12 \end{equation}

The code I have written to achieve this is the following:

x = var('x')
y = var('y')
g = function('g')(x,y) #symbolic function
f = g + 2*x
der_f = diff(f,x); der_f

and this is what I get:

diff(g(x, y), x) + 2

as I expected. However, I don't know how to follow. In particular, I need to know how to:

1) assign $\frac{dg(x,y)}{dx}\bigg\rvert_{x=0}=10$,

2) evaluate $\frac{df(x,y)}{dx}$ at $x=0$, so that I obtain $\frac{df(x,y)}{dx}\bigg\rvert_{x = 0} = 12$.