Calculus problem- Implicit differentiation

[thearn]

Homework Statement

e^y = x(y-1) answer must be in implicit form

Homework Equations

The Attempt at a Solution

I literally have no idea how to do this problem. I have the answer, but that's it.
The answer is dy/dx(e^y) = x(dy/dx) + y - 1

 

[jedishrfu]

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

 

[Fredrik]

I think that would be "your other left".

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

 

[jedishrfu]

I think that would be "your other left".

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

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

 

[SammyS]

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

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

 

[jedishrfu]

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

Yeah, I wear Tevas now.

 

[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.

 

[Fredrik]

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.

 

[X89codered89X]

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.

how bout now?

 

[Fredrik]

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
$$\frac{d}{dx}\phi(y(x),x) =\frac{\partial\phi}{\partial y}\frac{dy}{dx} +\frac{\partial\phi}{\partial x}.$$

 

[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 I'm pretty sure it originally made sense.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?

 

[Fredrik]

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.

 

[SammyS]

...

I might as well just delete my post.
Edit: Actually on that note, is it possible to delete posts or just edit them?

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.

 

[HallsofIvy]

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

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

 

[jedishrfu]

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

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