# Calculus problem- Implicit differentiation

1. Mar 22, 2013

### thearn

1. The problem statement, all variables and given/known data
e^y = x(y-1) answer must be in implicit form

2. Relevant equations

3. The attempt at a solution
I literally have no idea how to do this problem. I have the answer, but thats it.
The answer is dy/dx(e^y) = x(dy/dx) + y - 1

2. Mar 22, 2013

### Staff: Mentor

I think you differentiate both sides and on the left side use the product rule.

3. Mar 22, 2013

### Fredrik

Staff Emeritus
I think that would be "your other left".

Chain rule on the left, product rule on the right.

4. Mar 22, 2013

### Staff: Mentor

Yeah sorry I'm somewhat dislexic. My mother would paint a red dot on my right shoe so I'd get it right.

5. Mar 22, 2013

### SammyS

Staff Emeritus
I suppose you've out grown those shoes by now.

6. Mar 22, 2013

### Staff: Mentor

Yeah, I wear Tevas now.

7. Mar 22, 2013

### X89codered89X

I think the best way to do this is to remember that everything is a function of x. It's just a slightly obscure application of product and chain rule.

Last edited: Mar 23, 2013
8. Mar 22, 2013

### Fredrik

Staff Emeritus
You're giving away too much information X89. That first equality was the only thing we left for the OP to figure out on his own.

9. Mar 22, 2013

### X89codered89X

how bout now?

10. Mar 23, 2013

### Fredrik

Staff Emeritus
That's better. However, you are using the symbol $\phi$ inconsistently. Your notations suggest that it's first a function from ℝ into ℝ, and then a function from ℝ2 into ℝ. And if $\phi:\mathbb R^2\to\mathbb R$, then the last equality isn't true in general. It's true when $\phi$ is defined by $\phi(y(x),z)=e^{y(x)}$ for all $x,z\in\mathbb R$, because this $\phi$ is actually independent of the second variable, but in general
$$\frac{d}{dx}\phi(y(x),x) =\frac{\partial\phi}{\partial y}\frac{dy}{dx} +\frac{\partial\phi}{\partial x}.$$

11. Mar 23, 2013

### X89codered89X

Ah, yeah I see what you mean. When I was deleting stuff from my original post I didn't do a very careful job at all. I'm pretty sure it originally made sense. I might as well just delete my post.
Edit: Actually on that note, is it possible to delete posts or just edit them?

12. Mar 23, 2013

### Fredrik

Staff Emeritus
Give me a second. I'll see if I can delete this one.

Nope. When I click edit and go into advanced mode, I don't see a delete option. I think the admins have disabled the edit feature in the homework forums to prevent people from deleting the evidence that they got help from someone.

When you delete a post from another forum, the moderators can still see it, so if you have written something really embarassing, edit out the contents first, save the changes, and then delete.

13. Mar 23, 2013

### SammyS

Staff Emeritus
For one thing, in my experience, it's not possible to delete a post after you can no longer "Edit" it. I think that's after something like 700 minutes.

More importantly, according to the rules of this Forum, you are not allowed to delete the Original Post of a thread -- especially after someone has responded to it. Doing such will result in a warning or infraction from the Moderators.

14. Mar 23, 2013

### HallsofIvy

You're lucky. My mother would just stomp on my left foot. (Or was that my drill sergeant? I keep getting them confused.)

15. Mar 23, 2013

### Staff: Mentor

How'd you know my Mom was a drill sgt? Hey just kidding Mom. Mom? Gotta go... Hup Two three four...