$f(x+\frac{y}{2})-f(x-\frac{y}{2})=2x^2y+5y^2$
$\frac{d f(3)}{dx}= f'(3)=?$
As there is no information on whether $y$ is a function or a constant, I believe it must be treated as a constant. Then, we need to know the value of $y$ in order to set $x+\frac{y}{2}=3$ and find the derivative.
How can we solve this problem?
$$ \frac{df(x)}{dx} = \lim_{y \to 0} \left(\frac{f(x + \frac{y}{2}) - f(x - \frac{y}{2})}{y}\right) = \lim_{y \to 0} \frac{2x^2y + 5y^2}{y} = \lim_{y \to 0} 2x^2 + 5y = 2x^2 $$
Therefore $f'(3) = 18$