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•  » Differentiation problems (please solve with steps)

## #1 2013-04-27 13:18:45

Omar Desoky
Guest

### Differentiation problems (please solve with steps)

Dears,

(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 2013-04-27 13:20:49

bobbym

Online

### 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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #3 2013-04-27 13:50:46

Agnishom
Real Member

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### 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'
'The whole person changes, why can't a habit?' -Alokananda

## #4 2013-04-27 14:36:46

Agnishom
Real Member

Offline

### 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'
'The whole person changes, why can't a habit?' -Alokananda

## #5 2013-04-27 15:46:13

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 2013-04-27 15:49:57

bobbym

Online

### 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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.
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