Elementary calculus equation

Question

If I have $L = y^2(1-y')^2$ are the following partial derivatives correct? Wolfram Alpha tells me otherwise... $$\frac{\partial L}{\partial y} = 2y - 4yy' + 2y{y'}^2$$ $$\frac{\partial L}{\partial y'}= -2y^2 + 2y^2y'$$ I'm mainly unsure about the second partial. This is part of a broader question where I am solving the Euler-Lagrange equation.

Answer 1

If you're treating $y$ and $y'$ as separate variables, then yes, you are correct. I suspect Wolfram Alpha doesn't know that $y$ and $y'$ are to be considered as separate variables. It would give the correct answer if you used, say, $z$ instead of $y'$.