Given $(5x+5y~)^3= 125x^3+125y^3$, find the derivative.
Using the chain rule and power rule, I came up with
$3(5x+5y)^2 \cdot (\frac{d}{dx}5x+\frac{dy}{dx}5y)= 3 \cdot 125x^2 +3 \cdot 125y^2$
Now, the derivative of $5x~$ is 5, but what about the derivative of $5y~$?
I know that $\frac{dy}{dx}5y~$ turns to $5(\frac{dy}{dx}(y~))$
What happens after that? When I plugged the formula into Wolfram Alpha to double check my steps, it says that $\frac{dy}{dx}(y~)=0$ What is the reasoning behind that?