How to take derivative? Find a curve passing through (0,0) and (1,1) that is an extremal of the function
$${\rm J}\left(x,y,y'\right)=
\int_{0}^{1}\left[ y'^{\,2}\left(x\right ) + 12\,x\,{\rm y}\left(x\right)\right]\,{\rm d}x$$
I am very confused how to take the derivative:
$$\frac{\partial f}{\partial y} - \frac{d}{dx}\left(\frac{\partial f}{\partial y'}\right) = 0.$$
I got $12x+12y*2y^2=0$, which doesn't seem right. Could someone write out the differentiation?

$f(x,y,y')=y'^2+12xy$, so you want $12x+(2y')'=0$.
