Implicit differentiation homework

1. Nov 8, 2008

UNknown 2010

hi

i couldn't solve this question
i think there is a mistake in it
anyone can check it please ?

2. Nov 8, 2008

HallsofIvy

Staff Emeritus
Re: differentiation

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. Nov 8, 2008

UNknown 2010

Re: differentiation

then I got stuck

4. Nov 8, 2008

gabbagabbahey

Re: differentiation

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

5. Nov 8, 2008

tiny-tim

And 5y = … ?

6. Nov 12, 2008

JANm

Re: differentiation

5y=2x/(x+1)

7. Nov 12, 2008

tiny-tim

Yup!

So dy/dx = (5y - 2)/-5(x+1) = … ?

8. Nov 12, 2008

JANm

Re: differentiation

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. Nov 12, 2008

tiny-tim

Sorry, not following you.

btw, are you the same person as UNknown 2010?

10. Nov 12, 2008

JANm

Re: differentiation

No I am knot!

11. Nov 12, 2008

gabbagabbahey

Re: differentiation

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

12. Nov 14, 2008

Mentallic

Re: differentiation

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)

Last edited: Nov 14, 2008
13. Nov 14, 2008

tiny-tim

Hi Mentallic!

I think your way is better!!