So I'm trying to differentiate an equation using implicit differentiation.

I start with ${e}^{x/y}=7x-y$

Now the left side of the eqn is where I'm having trouble.

I tried to use differentiation rules for exponentials, but this is incorrect.

Here's what I tried though:

$({e}^{x}{)}^{1/y}\mathrm{ln}({e}^{x}){y}^{\prime}=7-{y}^{\prime}$

simplfied to:

$x({e}^{x}{)}^{1/y}\cdot {y}^{\prime}=RS$

I start with ${e}^{x/y}=7x-y$

Now the left side of the eqn is where I'm having trouble.

I tried to use differentiation rules for exponentials, but this is incorrect.

Here's what I tried though:

$({e}^{x}{)}^{1/y}\mathrm{ln}({e}^{x}){y}^{\prime}=7-{y}^{\prime}$

simplfied to:

$x({e}^{x}{)}^{1/y}\cdot {y}^{\prime}=RS$