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Implicit differentiation homework

  • #1
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 [Broken]
 
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Answers and Replies

  • #2
HallsofIvy
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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.
 
  • #3


http://img394.imageshack.us/img394/7196/94146936ef8.png [Broken]
then I got stuck
 
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  • #4
gabbagabbahey
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Now solve your original equation for y and substitute it into your result.
 
  • #5
tiny-tim
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dy/dx = (5y - 2)/-5(x+1)
then I got stuck
And 5y = … ? :smile:
 
  • #6
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5y=2x/(x+1)
 
  • #7
tiny-tim
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5y=2x/(x+1)
Yup! :smile:

So dy/dx = (5y - 2)/-5(x+1) = … ? :wink:
 
  • #8
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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.
 
  • #9
tiny-tim
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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
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No I am knot!
 
  • #11
gabbagabbahey
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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
Mentallic
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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)
 
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  • #13
tiny-tim
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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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