Calculus problem- Implicit differentiation

In summary, the student's mother would paint a red dot on his right shoe so he would know which foot to use when doing exercises at home. His mother is a drill sergeant.
  • #1
thearn
27
0

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
 
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  • #2
I think you differentiate both sides and on the left side use the product rule.
 
  • #3
I think that would be "your other left". :wink:

Chain rule on the left, product rule on the right.
 
  • #4
Fredrik said:
I think that would be "your other left". :wink:

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.
 
  • #5
jedishrfu said:
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.
 
  • #6
SammyS said:
I suppose you've out grown those shoes by now.

Yeah, I wear Tevas now.
 
  • #7
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:
  • #8
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
Fredrik said:
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?
 
  • #10
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
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 I'm pretty sure it originally made sense.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
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. :smile:
 
  • #13
X89codered89X said:
...

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.
 
  • #14
jedishrfu said:
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.)
 
  • #15
HallsofIvy said:
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...
 

1. What is implicit differentiation?

Implicit differentiation is a method used in calculus to find the derivative of a function that is not in the form of y= f(x). Instead, the equation may have both x and y variables, and the derivative is found by treating y as a function of x and using the chain rule.

2. When should implicit differentiation be used?

Implicit differentiation is typically used when the equation cannot be easily solved for y in terms of x. It is also useful when dealing with equations that have both x and y variables and cannot be easily separated into two functions.

3. How is implicit differentiation different from explicit differentiation?

Explicit differentiation is used to find the derivative of a function that is in the form of y= f(x), where y is explicitly defined in terms of x. Implicit differentiation, on the other hand, is used for functions where y is not explicitly defined in terms of x.

4. What is the chain rule and how is it used in implicit differentiation?

The chain rule is a calculus rule used to find the derivative of composite functions. In implicit differentiation, the chain rule is used to find the derivative of the y variable, treating it as a function of x. This allows us to find the derivative of the entire equation.

5. What are some common mistakes when using implicit differentiation?

Some common mistakes when using implicit differentiation include not properly applying the chain rule, not taking the derivative of both sides of the equation, and forgetting to include the derivative of the y variable in the final answer. It is important to double check the steps and make sure all variables are accounted for in the final derivative.

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