Question

Find dy/dx with implicit differentiation:

e^(x/y)=2x-y

Answer 1

d/dx [e^(x/y)] = d/dx [2x - y]



[ d/dx [(x/y)] ] * e^(x/y) = 2 - dy/dx
[1/y - (x/y^2) * dy/dx] * e^(x/y) = 2 -dy/dx
now isolate dy/dx ..

Answer 2

http://www.wolframalpha.com/input/?i=differentiate+in+respect+to+x+e%5E%28x%2Fy%29%3D2x-y

Answer 3

oh I see I didnt treat x/y as a function

Answer 4

or rather y as a function in x/y

Answer 5

Here we need to use the chain rule to solve the that...

Answer 6

just want to check myself as well isolating dy/dx from my expression gives :
[1/y - (x/y^2) * dy/dx] * e^(x/y) = 2 -dy/dx

dy/dx ( 1 - (x/y^2)e^(x/y) )= 2 - [e^(x/y)]/ y
dy/dx = [ 2y- e^(x/y) ]/[ (y - x/y)e^(x/y) ]

Answer 7

yes same as pavanneella (i can multiply num and denom by y)

Answer 8

Thanks to all!