Good evening, I'm struggling on a problem about jacobian and composed functions : They give a function $ g(r,\phi) = (rcos(\phi),rsin(\phi)) $
And a the jacobian of a function $f_2$ that is defined as :
$f_2 = f \circ g $ (They give $J_{f_2}$)
Then the sample problem ask to find $\partial f /\partial x$ (not $f_2$)
I thought of calculating the jacobian of Jg and try to get $J_f = J_{f_2}*J_g^{⁻1}$ Then saying $x=rcos(\phi)$ and $y = rsin(\phi) $ But it doesn't work. I already know the answer but It's very hard to find a way to get to it. Thanks in advance