# Implicit differentiation homework

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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HallsofIvy
Homework Helper

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 [Broken]
then I got stuck

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gabbagabbahey
Homework Helper
Gold Member

Now solve your original equation for y and substitute it into your result.

tiny-tim
Homework Helper
dy/dx = (5y - 2)/-5(x+1)
then I got stuck
And 5y = … ? 5y=2x/(x+1)

tiny-tim
Homework Helper
5y=2x/(x+1)
Yup! So dy/dx = (5y - 2)/-5(x+1) = … ? 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.

tiny-tim
Homework Helper
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. btw, are you the same person as UNknown 2010?

No I am knot!

gabbagabbahey
Homework Helper
Gold Member

No I am knot!
You're "a method for fastening or securing linear material such as rope by tying or interweaving."? \

Disclaimer: (1) Comment said in jest. (2) Quote is the definition of the term 'knot', taken from wiki Mentallic
Homework Helper

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:

$$2x-5y=5xy$$

$$y(5x+5)=2x$$

$$y=\frac{2x}{5(x+1)}$$

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

EDIT: Felt like I was giving away the answer (literally)

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tiny-tim
Hi Mentallic! I think your way is better!! 