Implicit differentiation homework

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Homework Help Overview

The discussion revolves around a problem involving implicit differentiation, where participants are attempting to differentiate an equation with respect to x. The original poster expresses uncertainty about the problem's setup and seeks verification from others.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the process of implicit differentiation, with some providing derivatives and others suggesting substitution methods. Questions arise about the correctness of the original equation and the steps taken so far.

Discussion Status

There is an ongoing exchange of ideas, with some participants offering guidance on differentiation techniques and substitution. Multiple interpretations of the problem are being explored, but no consensus has been reached on the best approach.

Contextual Notes

Some participants express confusion about the problem's details and the methods suggested, indicating a lack of clarity in the original equation and its implications for differentiation.

UNknown 2010
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hi

i couldn't solve this question
i think there is a mistake in it
anyone can check it please ?
http://img296.imageshack.us/img296/3716/13055173zr3.png
 
Last edited by a moderator:
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Use implicit differentiation:
The derivative of 5y, with respect to x, is 5 dy/dx and the derivative of 5xy, with respect to x, is 5y+ 5x dy/dx.

Differentiate both sides of the equation with respect to x and solve for dy/dx.
 


http://img394.imageshack.us/img394/7196/94146936ef8.png
then I got stuck
 
Last edited by a moderator:


Now solve your original equation for y and substitute it into your result.
 
UNknown 2010 said:
dy/dx = (5y - 2)/-5(x+1)
then I got stuck

And 5y = … ? :smile:
 


5y=2x/(x+1)
 
JANm said:
5y=2x/(x+1)

Yup! :smile:

So dy/dx = (5y - 2)/-5(x+1) = … ? :wink:
 


Tiny Tim
Ever heard of substitution: instead of 5y in the differential equation you may substitute
2x/(x+1) while the first equation seems to be right.
 
JANm said:
Tiny Tim
Ever heard of substitution: instead of 5y in the differential equation you may substitute
2x/(x+1) while the first equation seems to be right.

Sorry, not following you. :confused:

btw, are you the same person as UNknown 2010?
 
  • #10


No I am knot!
 
  • #11


JANm said:
No I am knot!

You're "a method for fastening or securing linear material such as rope by tying or interweaving."? :confused:\

Disclaimer: (1) Comment said in jest. (2) Quote is the definition of the term 'knot', taken from wiki :smile:
 
  • #12


I don't know if you might prefer this method, but this is how I would've done it since I don't have a clue about what everyone else has suggested:

[tex]2x-5y=5xy[/tex]

[tex]y(5x+5)=2x[/tex]

[tex]y=\frac{2x}{5(x+1)}[/tex]

Now just use the quotient rule. [tex]\frac{dy}{dx}=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}[/tex] where u=numerator, v=denominator.

EDIT: Felt like I was giving away the answer (literally)
 
Last edited:
  • #13
Mentallic said:
I don't know if you might prefer this method, but this is how I would've done it since I don't have a clue about what everyone else has suggested …

Hi Mentallic! :smile:

I think your way is better! :biggrin:
 

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