Find the derivative of f(x)=-9/x at x=-4
@agent0smith @jim_thompson5910 @Phebe @e.mccormick

Question

Find the derivative of f(x)=-9/x at x=-4
@agent0smith @jim_thompson5910  @Phebe  @e.mccormick

jim_thompson5910 · Answer

First find the derivative of f(x)=-9/x

anonymous · Answer

That's excatly what i dont know how to do >.<

jim_thompson5910 · Answer

think of -9/x as -9x^(-1)

jim_thompson5910 · Answer

then use the idea that if y = x^n, then y ' = n*x^(n-1)

e.mccormick · Answer

That is called the power rule.  Have you been taught that yet?

anonymous · Answer

i have not

e.mccormick · Answer

OK.  What are you using at this point to do derivatives?  The limit definition?

anonymous · Answer

i think i got is ...4/9?

e.mccormick · Answer

I do not get that answer.

Are you using $f'(x)=\lim\limits_{\Delta x\rightarrow 0}\dfrac{f(x+\Delta x)-f(x)}{\Delta x}$ to find derivatives?

anonymous · Answer

yes.. im redoing it

anonymous · Answer

16/9

e.mccormick · Answer

OK.

anonymous · Answer

i think im wrong again

e.mccormick · Answer

How did you get it with 16 on the top and 9 on the bottom?

anonymous · Answer

i honestly think im doing the work wrong

anonymous · Answer

i redid it... 9/16?

anonymous · Answer

please tell me thats right because im literally dying lolol

e.mccormick · Answer

You got it.  I am going to show you how the thing Jim talked about works:

$\dfrac{d}{dx}x^n=nx^{n-1}$

$\dfrac{d}{dx}\dfrac{-9}{x} \implies \dfrac{d}{dx}-9x^{-1}$

$\dfrac{d}{dx}-9x^{-1} \implies -9\left( \dfrac{d}{dx}x^{-1}\right )$

Now I use the rule above.

$-9\left( \dfrac{d}{dx}x^{-1}\right) = -9\left( -1x^{-1-1}\right)$

Which simplifies to:

$9x^{-2}$

or:

$\dfrac{9}{x^2}$

e.mccormick · Answer

And at -4, that is $\dfrac{9}{16}$

anonymous · Answer

Wow that is way easier than what i was trying to do.. THANK YOU SO MUCH♥

e.mccormick · Answer

Well, you need to learn why it works still.  They teach math in steps.  You learn addition before multiplication.  Multiplication is just repeated addition.  You will learn the power rule soon enough.  But seeing it, you have a way to check your work.

anonymous · Answer

YES honestly thank you, math is my weakness haha

anonymous · Answer

@e.mccormick

anonymous · Answer

Find the derivative of f(x) = 4/ x at x = 2
I GOT 4 can you tell me if thats good?

anonymous · Answer

@jim_thompson5910  @e.mccormick

jim_thompson5910 · Answer

deriving 4/x gives you ???

jim_thompson5910 · Answer

think of 4/x as 4x^(-1)

anonymous · Answer

Wait... im i completly wrong?

jim_thompson5910 · Answer

what did you get for f ' (x)

anonymous · Answer

-1

jim_thompson5910 · Answer

when you use the power rule to derive x^(-1), you get ???

anonymous · Answer

wait... -4

jim_thompson5910 · Answer

Here's how I think of the power rule

|dw:1400110066022:dw|

jim_thompson5910 · Answer

pull down the exponent

|dw:1400110207950:dw|