# Thread: Diff questions

1. ## Diff questions

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

2. 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

3. 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

4. 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

5. 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

6. Oh! Hi there Captain!

-Dan

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

8. 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!

9. No sadly I am not , I want to waste more of your precious air...

That line refers to morons that do drugs and crap.

10. 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?

11. Yep thats for my clan