Diff questions

**NeF** · July 20th 2006, 01:21 PM

I want to double check these answers, this book doesnt supply answers.

1
$y= \frac{5x^4-3x}{x^2}\$
$y= 4x^2-2x^-1$
$\frac{dy}{dx}\ = 8x+2x^-2$
$8x+\frac{2}{x^2}\$

2
$f(x)=(\frac{1}{x^2}+2)(x-3)$
$f(x)=(x^-2+2)(x-3)$
$f(x)= x^-1-3x^2+2x-6$
$f'(x)= x^-1-6x^-3+2$
$= \frac{-1}{x^2}\ + \frac{6}{x^3}+2$

3
$y= \frac{2\sqrt(x)}{x}$
$y= 2x^\frac{-1}{2}$
$\frac{dy}{dx} = -x^\frac{-3}{2}$
$= -\frac{1}{x^\frac{3}{2}}$

Thanx in advance

**topsquark** · July 20th 2006, 01:41 PM

Originally Posted by NeF

I want to double check these answers, this book doesnt supply answers.

1
$y= \frac{5x^4-3x}{x^2}\$
$y= 4x^2-2x^-1$
$\frac{dy}{dx}\ = 8x+2x^-2$
$8x+\frac{2}{x^2}\$

Your second line is wrong. Given your second line, your third and fourth lines are correct.
$y = 5x^2 - 3x^{-1}$

Since you've evidently got the rules right, I'll let you finish it.

-Dan

**CaptainBlack** · July 20th 2006, 01:42 PM

Originally Posted by NeF

I want to double check these answers, this book doesnt supply answers.

1
$y= \frac{5x^4-3x}{x^2}\$
$y= 4x^2-2x^-1$
$\frac{dy}{dx}\ = 8x+2x^-2$
$8x+\frac{2}{x^2}\$

It's not entirely clear what you are asking, but here I will assume that
you want the derivative of:

$y= \frac{5x^4-3x}{x^2}\$

First divide through on the right hand side by the $x^2$ at the bottom:

$y= 5x^2-3x^{-1}\$

Now differentiate using the rules for differentiating powers:

$\frac{dy}{dx}\ = 10x+3x^{-2}$

Now rearrange and simplify (back towards something like the form we started
from):

$\frac{dy}{dx}\ = 10x+\frac{3}{x^{2}}$

$\frac{dy}{dx}\ = \frac{10x^3+3}{x^{2}}$

RonL

**topsquark** · July 20th 2006, 01:50 PM

Originally Posted by NeF

I want to double check these answers, this book doesnt supply answers.

2
$f(x)=(\frac{1}{x^2}+2)(x-3)$
$f(x)=(x^-2+2)(x-3)$
$f(x)= x^-1-3x^2+2x-6$
$f'(x)= x^-1-6x^-3+2$
$= \frac{-1}{x^2}\ + \frac{6}{x^3}+2$

Your third line is wrong. (Typo?) Given that then your derivative is wrong. However, your final answer is correct.

$f(x)= x^{-1}-3x^{-2}+2x-6$
$f'(x)= -x^{-2}+6x^{-3}+2$

Also, you might look into the product rule to do this one:
$f(x)=(\frac{1}{x^2}+2)(x-3)$
$f'(x) = \frac{-2}{x^3}(x-3) + \left ( \frac{1}{x^2}+2 \right ) \cdot 1$
$f'(x) = \frac{-2x + 3}{x^3} + \frac{1+2x^2}{x^2}$
etc, etc...

-Dan

**topsquark** · July 20th 2006, 01:51 PM

Originally Posted by NeF

I want to double check these answers, this book doesnt supply answers.

3
$y= \frac{2\sqrt(x)}{x}$
$y= 2x^\frac{-1}{2}$
$\frac{dy}{dx} = -x^\frac{-3}{2}$
$= -\frac{1}{x^\frac{3}{2}}$

This one looks okay. By the way, note the use of the {} in the Tex in the preceeding messages.

-Dan

**topsquark** · July 20th 2006, 01:52 PM

Oh! Hi there Captain!

-Dan

**NeF** · July 23rd 2006, 08:34 PM

Hectic, Thanks alot again for seeing all the stupid mistakes I am making.

**ThePerfectHacker** · July 24th 2006, 11:04 AM

Originally Posted by NeF

Hectic, Thanks alot again for seeing all the stupid mistakes I am making.

Does that mean you are going to kill yourself now!

**NeF** · July 24th 2006, 11:07 AM

No sadly I am not

, I want to waste more of your precious air...

That line refers to morons that do drugs and crap.

**ThePerfectHacker** · July 24th 2006, 11:17 AM

Originally Posted by NeF

That line refers to morons that do drugs and crap.

Then why do you have a picture of Raiden over there? You clan thing?

**NeF** · July 24th 2006, 11:30 AM

Yep thats for my clan

Thread: Diff questions

LinkBack

Thread Tools

Display

Diff questions

Similar Math Help Forum Discussions

Diff Eq. x' = t * cos(t)²

Diff eq IVP

diff eq's

diff eq help!

diff eq help

Search Tags