Question

How do you use imlicit differentiation to differentiate e^(xy)?

I have the problem "use implicit differentiation to find dy/dx.
e^(xy)+ x^2 - y^2 = 10. I've gotten to the point whereI have d/dx(e^(xy)) + 2x - 2ydy/dx = 0, but I can't go any further because I don't know how to use implicit differentiation to find e/dx(e^(xy)). It's been a while since I've done this and i don't remember, can someone refresh my memory? Thanks1

Answer 1

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

e^(xy) (xdy/dx + y) + 2x - 2y dy/dx = 0

xe^(xy) dy/dx + ye^(xy) + 2x - 2y dy/dx = 0

dy/dx (xe^(xy) - 2y) = -2x - ye^(xy)

dy/dx = (2x + ye^(xy) ) / (2y - xe^(xy) )