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

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

Mathematics
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ill help but you also have to try.
ok sure
The answer is e3x√(32x−1/2) e3x(32x−1/2)

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Now I need a medal
@Redneckk__Lifee but how you get that
online duhh. and why did you ask my name you already know it.
I'm pretty sure I'm waiting for a medal!!!!!!
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 nope its wrong
I meant- did i type your QUESTION correctly
|dw:1443775238584:dw|
so its \[f(x) = 3\sqrt{x} - \frac{ 1 + x }{ x^4 }\] ???
nope
no, I mean is that the question?
yes it is
ok wait a sec
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?
@FireKat97 wait a sec
okay just tag me back whenever you're ready :)
|dw:1443777396971:dw|
here is the question
ok so we need to find the derivative of this
so its just like the one I'd typed up above?
oh yeah know i see
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?
sorry about that
nah, no problem :)
|dw:1443777684653:dw|
haha
wait but why do we move 4
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?
I find it easier to move it to the top, distribute it and then differentiate each of the terms
I'll show you what I mean
yeah plz i am confuse
\[f(x) = 3\sqrt{x} - \frac{ 1 + x }{ x^4 }\] = \[3\sqrt{x} - x ^{-4} (1 + x)\] do you see what I did here?
yeah know that's make a lot of scence
I simply brought the x^-4 into the numerator position and am now going to distribute it
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
do you see how I got that?
wait how you get -x^3
oh i got u
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, \[(-x^{-4}).(x^1) = -x^{-4 + 1} = -x^{-3} \]
and now we have three separate terms, which we can differentiate
@MTALHAHASSAN2 did you try differentiating?
oh yeah i am trying it
oh okay :)
so are we left up with 3sqrt -x^-4 -x^-3
yup
and know we have to differentiating?
right
yeah we differentiate each of the terms
so for the sqrt is it be 1/2sqrt x
close
|dw:1443779376906:dw|
yup thats right!
and what about the x
the \[-x^{-4} - x^{-3}\]??
is it goona go in the denominater
we haven't differentiated those two terms yet..
not quite...
do you want me to show you?
yes plz
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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