Question

Find y′ by implicit differentiation. e^(x/y)=3x-4y

Answer 1

find the y'

Answer 2

Show us your best guess first. Then we'll help.

Answer 3

Right @mathmale ?

Answer 4

Suggestion: Apply the derivative operator, (d/dx), to both sides of your equation. Treat x as the independent variable and y as the dependent variable (that is, act as though y were a function of x, which requires application of the chain rule.

It'd help you, as well as possible helpers, if you'd please share your first tentative efforts towards finding the derivative.

Answer 5

i'm guessing the only thing troubling you is the e^(x/y) ? :P

Answer 6

uh, I dont get how to derivative the e^x/y

Answer 7

yep, you are right.@iambatman

Answer 8

Hints: (d/dx)e^x= e^x
(d/dx)e^u = e^u * (du/dx) (Chain rule)

Answer 9

^^

Answer 10

That exponent, (x/y) is itself a function, and in particular is a quotient. Thus when you encounter x/y as the exponent, you'll need to apply the chain rule, which in turn requires that you apply the quotient rule. Mind giving this a stab?

Answer 11

sure, give me a sec,

Answer 12

I don't know if this will help you but, what are the derivatives of e^2x and e^(2/x)?

Answer 13

err e^(x/2)*

Answer 14

@iambatman e^2x=2e^x, e^(x/2)=same, is it right?

Answer 15

Nope

Answer 16

It's just chain rule, so what's the derivative of e^2x?

Answer 17

What would you say? e^x = e^x, so now if you have e^2x and apply the chain rule, you get?

Answer 18

so it would be e^2x=2e^2x

Answer 19

Exactly, so what's the derivative of e^(x/2)?

Answer 20

is it 1/2e^(x/2)

Answer 21

:), so what's the derivative of e^(x/y)?

Answer 22

is this right ? x/ye^x/y

Answer 23

ohh, so it would be 1/ye^x/y ?

Answer 24

What did you get as your final answer?

Answer 25

e^x/y=1-y^2 is this right?

Answer 26

d(x)3x-4y=1-y right?

Answer 27

i am still confused.....

Answer 28

1-y?

Answer 29

How'd you get that

Answer 30

bc 3 is constant and the x is 1

Answer 31

What's the derivative of 3x?

Answer 32

if 3 is constant, that means it's 0

Answer 33

Ok, but what's the derivative of 3x?

Answer 34

Oh I see what you're saying but, no that's not how it works.
I think you need to go over some derivative rules.
http://www.mathsisfun.com/calculus/derivatives-rules.html

Answer 35

Derivative of 3x = 3

Answer 36

The exponent of " e " in the original equation is itself a function:\[\frac{ x }{ y }.\] I strongly suggest you focus on this x/y for the time being. Use the Quotient Rule and Chain Rule to find the derivative (with respect to x) of this x/y.

Once you have this done, use the result in writing the derivative with respect to x of

\[e ^{\frac{ x }{ y }}\]

Answer 37

Sorry I didn't make this clear, I was just showing you how to get the basic derivatives, and once you figured that out, we could move to the actual problem itself :P. As @mathmale explained, that's how you would do it.

Answer 38

So, what did you get as your derivative for e^(x/y)?

Answer 39

1/y(e^x/y)

Answer 40

Use the chain rule

Answer 41

e^(x/y)*(x/y)'

Answer 42

ohhh, then i should use quotient on (x/y)' right?

Answer 43

Yes :P

Answer 44

(e^x/y)*(y-y')/y^2 is this right?