- #1

- 673

- 28

By chain rule,

##\frac{\partial y}{\partial x}=\frac{\partial y}{\partial g}\frac{\partial g}{\partial x}##

Using the reciprocity relation ##\frac{\partial y}{\partial g}=\Big(\frac{\partial g}{\partial y}\Big)^{-1}##, we have

##\frac{\partial y}{\partial x}=\frac{(\frac{\partial g}{\partial x})}{(\frac{\partial g}{\partial y})}##

This differs from the correct answer by a negative sign. What's wrong with this method?