Question

How do you differentiate `e^(xy) + x^2 - y^2 = 10`?

Answer 1

`dy/dx = - (y e^{xy} + 2x)/(x e^{xy} -2y)`

Explanation:

`e^(xy) + x^2 - y^2 = 10 = f(x,y)`

`f_x = y e^{xy} + 2x`

`f_y = x e^{xy} -2y`

by implicit function theorem:
`dy/dx = - (f_x)/(f_y) = - (y e^{xy} + 2x)/(x e^{xy} -2y)`