can how we find the derivative of the following function
3sqrt x -1+x/x^4

- MTALHAHASSAN2

can how we find the derivative of the following function
3sqrt x -1+x/x^4

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- anonymous

ill help but you also have to try.

- MTALHAHASSAN2

ok sure

- anonymous

The answer is e3x√(32x−1/2)
e3x(32x−1/2)

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## More answers

- anonymous

Now I need a medal

- MTALHAHASSAN2

@Redneckk__Lifee but how you get that

- anonymous

online duhh. and why did you ask my name you already know it.

- anonymous

I'm pretty sure I'm waiting for a medal!!!!!!

- marigirl

Okay so we are differentiating
\[\sqrt[3]{(x-1)}+ \frac{ x }{ x^4 }\]
Is that the equation? I want to make sure its correct before we begin

- marigirl

@MTALHAHASSAN2

- MTALHAHASSAN2

@marigirl nope its wrong

- marigirl

I meant- did i type your QUESTION correctly

- MTALHAHASSAN2

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- FireKat97

so its \[f(x) = 3\sqrt{x} - \frac{ 1 + x }{ x^4 }\]
???

- MTALHAHASSAN2

nope

- FireKat97

no, I mean is that the question?

- FireKat97

@MTALHAHASSAN2

- MTALHAHASSAN2

yes it is

- MTALHAHASSAN2

ok wait a sec

- FireKat97

okay, so what you want to start off doing, is bringing the \[x^4\] to the top, can you show me how you may do this?

- MTALHAHASSAN2

@FireKat97 wait a sec

- FireKat97

okay just tag me back whenever you're ready :)

- MTALHAHASSAN2

|dw:1443777396971:dw|

- MTALHAHASSAN2

here is the question

- MTALHAHASSAN2

ok so we need to find the derivative of this

- FireKat97

so its just like the one I'd typed up above?

- MTALHAHASSAN2

oh yeah know i see

- FireKat97

so firstly you want to start off by bringing the x^4 up to the top, can you do this and show me what you get?

- MTALHAHASSAN2

sorry about that

- FireKat97

nah, no problem :)

- MTALHAHASSAN2

|dw:1443777684653:dw|

- anonymous

haha

- MTALHAHASSAN2

wait but why do we move 4

- FireKat97

close, so I see you have brought up and distributed the x^4 and differentiated the 3x^1/2 and - x^-4, but you forgot about the - x^-3, do you see what i mean by this?

- FireKat97

I find it easier to move it to the top, distribute it and then differentiate each of the terms

- FireKat97

I'll show you what I mean

- MTALHAHASSAN2

yeah plz i am confuse

- FireKat97

\[f(x) = 3\sqrt{x} - \frac{ 1 + x }{ x^4 }\]
= \[3\sqrt{x} - x ^{-4} (1 + x)\]
do you see what I did here?

- MTALHAHASSAN2

yeah know that's make a lot of scence

- FireKat97

I simply brought the x^-4 into the numerator position and am now going to distribute it

- FireKat97

yup so now we can distribute it like so
\[3\sqrt{x} - x^{-4} - x^{-3}\]
and now we can differentiate each of the terms, have a go

- FireKat97

do you see how I got that?

- MTALHAHASSAN2

wait how you get -x^3

- MTALHAHASSAN2

oh i got u

- FireKat97

okay so when we open up \[-x^{-4} (1 + x)\]
we do \[-x^{-4} (1) -x^{-4} (x^1)\]
and according to index laws, when we multiply something with the same base, we add th powers, so for e.g. \[(a^2).(a^3) = a^5\] so in the same way, \[(-x^{-4}).(x^1) = -x^{-4 + 1} = -x^{-3} \]

- FireKat97

and now we have three separate terms, which we can differentiate

- FireKat97

@MTALHAHASSAN2 did you try differentiating?

- MTALHAHASSAN2

oh yeah i am trying it

- FireKat97

oh okay :)

- MTALHAHASSAN2

so are we left up with 3sqrt -x^-4 -x^-3

- FireKat97

yup

- MTALHAHASSAN2

and know we have to differentiating?

- MTALHAHASSAN2

right

- FireKat97

yeah we differentiate each of the terms

- MTALHAHASSAN2

so for the sqrt is it be 1/2sqrt x

- FireKat97

close

- MTALHAHASSAN2

|dw:1443779376906:dw|

- FireKat97

yup thats right!

- MTALHAHASSAN2

and what about the x

- FireKat97

the \[-x^{-4} - x^{-3}\]??

- MTALHAHASSAN2

is it goona go in the denominater

- FireKat97

we haven't differentiated those two terms yet..

- FireKat97

not quite...

- FireKat97

do you want me to show you?

- MTALHAHASSAN2

yes plz

- FireKat97

okay so you know how we have
\[f(x) = 3x^{1/2} -x^{-4} -x^{-3}\]
you did well in correctly being able to differentiate the first term, but we still have two terms left to differentiate so we should get
\[f'(x) = \frac{ 3 }{ 2\sqrt{x} } -(-4)x^{-4-1} -(-3)x^{-3-1} \]
which can further simplify down to
\[f'(x) = \frac{ 3 }{ 2\sqrt{x} } + 4x^{-5} + 3x^{-4}\]
does that make sense?

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