Split - Implicit differentiation(Help ASAP!)

[Zerrotolerance]

Ok, I need help again. I can not seem to figure out what to do when I need to use implict differentiation. My problem seems to come from trying to get the derivitive of a variable raise to a variable(sometimes divided by a variable) Excentially the same thing I struggled with above. Can someone show me how I would go about differentiating this implicitly:

e^(x/y) = 3x - y

I know to find the derivitive of both sides. I can't figure out the e^(x/y) because I need to use the quotient and chain rule somehow.

the right side is:

3-dy/dx

From there i think I would somehow get dy/dx all on one side to solve. Can someone please do this whole thing out so I can see all the steps and figure out what steps I am missing along the way. I have been working on my HW for 6 hours and can't seem to understand anything.

 

[Deleted member 4993]

Ok, I need help again. I can not seem to figure out what to do when I need to use implict differentiation. My problem seems to come from trying to get the derivitive of a variable raise to a variable(sometimes divided by a variable) Excentially the same thing I struggled with above. Can someone show me how I would go about differentiating this implicitly:

e^(x/y) = 3x - y

I know to find the derivitive of both sides. I can't figure out the e^(x/y) because I need to use the quotient and chain rule somehow.

the right side is:

3-dy/dx

From there i think I would somehow get dy/dx all on one side to solve. Can someone please do this whole thing out so I can see all the steps and figure out what steps I am missing along the way. I have been working on my HW for 6 hours and can't seem to understand anything.

Start a new thread for a new problem

\(\displaystyle \frac{d}{dx}\left [e^{\frac{x}{y}}\right ] \ = \ e^{\frac{x}{y}}\frac{d}{dx}\left [{\frac{x}{y}}\right ]\)

\(\displaystyle = \ e^{\frac{x}{y}}\left [{\frac{y - y'*x}{y^2}}\right ]\)

Now continue....