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## #1 2013-04-26 15:18:45

Omar Desoky
Guest

### Differentiation problems (please solve with steps)

Dears,

Answer each of the following:
(1) If y=x+1/x prove that x²(d²y/dx²)+x(dy/dx)=y
(2) Find the second derivative of (2x+3)/(3x-1) with respect ro (x-1)/(x+1)
(3) If y²=8/(1+x²) prove that (x²+1)(d²y/dx²)+3x(dy/dx)+y=0
(4) If y=(√x)+1/√x and z=(√x)-1/√x prove that d²y/dx²=(2x(y+2))/(x+1)³
(5) If y=cosx-3sinx prove that y'''+y''+y'+y=0

## #2 2013-04-26 15:20:49

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Differentiation problems (please solve with steps)

Hi;

http://www.mathisfunforum.com/viewtopic.php?id=14654

Please show a little bit of your work, or at least that you tried.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #3 2013-04-26 15:50:46

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,806
Website

### Re: Differentiation problems (please solve with steps)

Interesting, I will try

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #4 2013-04-26 16:36:46

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,806
Website

### Re: Differentiation problems (please solve with steps)

I can do 1, 4 and 5.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #5 2013-04-26 17:46:13

Omar Desoky
Guest

### Re: Differentiation problems (please solve with steps)

All is ok for me no problem about the final results but I only meed to make sure. of (2)
Thanls!

## #6 2013-04-26 17:49:57

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Differentiation problems (please solve with steps)

Hi Agnishom;

Let's do a simpler one so you can see the method.

Differentiate x^6 wrt x^2:

Say y = x^6, t =x^2

Now

Plugging in:

and that is the answer. There is an even simpler way involving a substitution.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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