Use implicit differentiation to find dy/dx . e^xy=8y

Question

Dy/dx= ?

Answer 1

e^xy=8y

Differentiate both sides w.r.x taking into account y =y(x) y is a function of x:

(e^xy)d(xy)=8 dy/dx

(e^xy)(y+xdy/dx)=8 dy/dx

Now in this equation find dy/dx

(xe^xy-8)(dy/dx)=y e^xy

dy/dx=y e^xy.(xe^xy-8)

Answer 2