Question

Find the partial derivative $\displaystyle{\frac{\partial z}{\partial y}}$ of the function $\displaystyle{z^{2}=x^2+y}$

Answer 1

$(z^{2})'{\scriptscriptstyle y} = (x^{2}+y)'{\scriptscriptstyle y}$

$2zz'{\scriptscriptstyle y} = 1$

${\frac {∂z} {∂y}}=z'{\scriptscriptstyle y}= {\frac 1 {2z}}$