Question

e^(xy) = xy find dy/dx​

Answer 1

Answer:

dy/dx =(1- xy)y/(1+xy)x

Step-by-step explanation:

e^xy = xy

taking log on both side

xy = logx + logy

xy - logy = logx

diffrenciating with respect to X we get

y + xdy/dx + (dy/dx)(1/y) = 1/x

dy/dx ( x + 1/y) = 1/x - y

dy/dx = (1- xy)y/(1+xy)x

Formula used

d(xy)/dx = ydx/dx + xdy/dx

Answer 2

Answer:

Step-by-step explanation:

e^(xy)=xy

Taking log both the sides

xy=logx+logy

Diff

Xdy/dx+y.1=1/x+1/y.dy/dx

(X-1/y)dy/dx=1/x-y

dy/dx=(1-xy)y/(xy-1)x

dy/dx=-y/x