Solution
= Solution
Apply the multivariable <chain rule> to a differentiable <function> $f(s,t)$ on the chosen local branch of the <parabolic coordinates>:
$$
\frac{\partial f}{\partial x}
=\frac{\partial f}{\partial s}\frac{\partial s}{\partial x}
+\frac{\partial f}{\partial t}\frac{\partial t}{\partial x}.
$$
Substituting part (ii) gives
$$
\boxed{\frac{\partial f}{\partial x}=\frac{t f_s+s f_t}{s^2+t^2},\qquad(s,t)\ne(0,0).}
$$