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#1 2013-04-27 13:18:45

Omar Desoky
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Differentiation problems (please solve with steps)

Dears,

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

#2 2013-04-27 13:20:49

bobbym
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Re: Differentiation problems (please solve with steps)

Hi;

Please read this:

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2013-04-27 13:50:46

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#4 2013-04-27 14:36:46

Agnishom
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Re: Differentiation problems (please solve with steps)

I can do 1, 4 and 5.
Please help with 2 and 3


'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'
'Who are you to judge everything?' -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
Administrator

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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
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