[SOLVED] Derivative help

**rawkstar** · October 5th 2009, 12:24 PM

i need to find the derivative of 4/sqrt (x)
Any help?

**e^(i*pi)** · October 5th 2009, 12:28 PM

Originally Posted by rawkstar

i need to find the derivative of 4/sqrt (x)
Any help?

$4x^{-\frac{1}{2}}$

Can be differentiated using the standard method

**rawkstar** · October 5th 2009, 12:33 PM

i'm just beginning my calc class so i dont know what that means
can someone help me find the derivative using the limit of the definition

**Plato** · October 5th 2009, 01:10 PM

Originally Posted by rawkstar

i'm just beginning my calc class so i dont know what that means
can someone help me find the derivative using the limit of the definition

Can you do algebra? Can you simplify the following?
$\frac{{\frac{4}{{\sqrt {x + h} }} - \frac{4}{{\sqrt x }}}}{h}$

**rawkstar** · October 5th 2009, 01:39 PM

Originally Posted by Plato

Can you do algebra? Can you simplify the following?
$\frac{{\frac{4}{{\sqrt {x + h} }} - \frac{4}{{\sqrt x }}}}{h}$

i know how to simplify the numerator
my problem is that i don't know how to simplify the denominator

**Plato** · October 5th 2009, 01:57 PM

Originally Posted by rawkstar

i know how to simplify the numerator
my problem is that i don't know how to simplify the denominator

Did you get $\frac{{\frac{4}{{\sqrt {x + h} }} - \frac{4}{{\sqrt x }}}}{h} = \frac{{4\sqrt x - 4\sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}?$

**rawkstar** · October 5th 2009, 02:14 PM

no

**Plato** · October 5th 2009, 02:17 PM

Originally Posted by rawkstar

no

Even so, do you understand how it was done? It is simple algebra.

**rawkstar** · October 5th 2009, 02:43 PM

i'm not sure how you're going about this problem, this is what i'm doing
((4/sqrt(x+h)) - (4/(sqrt(x))) / h then
(4 sqrt (x) - 4sqrt(x +h))/ (h)(x)(x + h) and im not sure where to go from here

i do know simple algebra, i'm not stupid, im just trying to solve this problem the way me teacher is instructing me to

**Plato** · October 5th 2009, 03:14 PM

Originally Posted by rawkstar

i'm not sure how you're going about this problem, this is what i'm doing
((4/sqrt(x+h)) - (4/(sqrt(x))) / h then
(4 sqrt (x) - 4sqrt(x +h))/ (h)(x)(x + h) and im not sure where to go from here
i do know simple algebra, i'm not stupid, im just trying to solve this problem the way me teacher is instructing me to

I have taught calculus courses off and on since 1964.
The concepts of calculus in and of themselves are easy to understand.
So what makes so hard for so many students?
One simple fact: students with poor algebra skills don’t get it.

**rawkstar** · October 5th 2009, 03:33 PM

whatever, i solved it by myself

**Power of One** · October 5th 2009, 03:34 PM

Originally Posted by Plato

Did you get $\frac{{\frac{4}{{\sqrt {x + h} }} - \frac{4}{{\sqrt x }}}}{h} = \frac{{4\sqrt x - 4\sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}?$

Wow, I had this same exact problem for homework and I don't know how to do it either!!! xD

Using the definition of a derivative method and not the power of the rule, you would then have to find the limit of the right side expression as it approaches h. If you plug in zero for h, you get 0 in the denominator. So what do you do from there since you can't factor?

**hjortur** · October 5th 2009, 04:07 PM

You can do it like this Power of One

$ \frac{{4\sqrt x - 4\sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}=4\frac{{\sqrt x - \sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}\cdot \frac{\sqrt x + \sqrt {x + h}}{\sqrt x + \sqrt {x + h}} = 4\frac{x-(x+h)}{h\sqrt x \sqrt {x + h}}\cdot\frac{1}{\sqrt x + \sqrt {x + h}}= $

$ 4\frac{-h}{h\sqrt x \sqrt {x + h}}\cdot\frac{1}{\sqrt x + \sqrt {x + h}}= \frac{-4}{(\sqrt x \sqrt {x + h})(\sqrt x + \sqrt {x + h})} $

Now taking the limit

$ \lim\limits_{h\to0}\frac{-4}{(\sqrt x \sqrt {x + h})(\sqrt x + \sqrt {x + h})}=\frac{-4}{x\cdot2\sqrt{x}}=\frac{-2}{x\sqrt{x}} $

Hope that helps.

**Plato** · October 5th 2009, 05:03 PM

Originally Posted by hjortur

$ \frac{{4\sqrt x - 4\sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}=4\frac{{\sqrt x - \sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}\cdot \frac{\sqrt x + \sqrt {x + h}}{\sqrt x + \sqrt {x + h}} = 4\frac{x-(x+h)}{h\sqrt x \sqrt {x + h}}\cdot\frac{1}{\sqrt x + \sqrt {x + h}}= $
$ 4\frac{-h}{h\sqrt x \sqrt {x + h}}\cdot\frac{1}{\sqrt x + \sqrt {x + h}}= \frac{-4}{(\sqrt x \sqrt {x + h})(\sqrt x + \sqrt {x + h})} $

Now taking the limit

$ \lim\limits_{h\to0}\frac{-4}{(\sqrt x \sqrt {x + h})(\sqrt x + \sqrt {x + h})}=\frac{-4}{x\cdot2\sqrt{x}}=\frac{-2}{x\sqrt{x}} $

You are a spoilsport.
Do you care if someone learns something?
Or do you just want to show us what you can do?

**hjortur** · October 5th 2009, 05:20 PM

I am sorry if I have ruined this one. He was asking for help and sounded like he was stuck. In hindsight I probarbly should have just posted the first few steps.
I am not a showoff, and am very sorry if I have come across as one.

Should I edit the original post and remove the solution?

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