Question

find the derivative of the following function

Answer 1

\[y=\frac{ 3+2x-8\sqrt{x} }{ x }\]

Answer 2

Just quotient rule away :)
\[\huge \frac{d}{dx}\frac{f(x)}{g(x)}=\frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}\]

Answer 3

or , easier ... bring x from the denominator to the top as x^-1

Answer 4

divide

Answer 5

y=3x^-1+2 -8x^(-1/2)

Answer 6

what?

Answer 7

I reckon it is easier, after all.
\[\Large \frac{3+2x-8\sqrt{x}}{x}=\frac3x+2-\frac8{\sqrt{x}}=3x^{-1}+2-8x^{-\frac12}\]
And just power rule away, this time :)
\[\huge \frac{d}{dx}ax^n=nax^{n-1}\]

Answer 8

idk any of the rules, I'm taking calculus online and the teacher doesn't help with or explain anything.

Answer 9

Well, the gist of it is, when the derivative of
\[\huge ax^n\]You just bring down the exponent n, and multiply it to ax, and then, subtract one from the original exponent
\[\huge nax^{n-1}\]

For example, the derivative of 4x^3
\[\huge \frac{d}{dx}4x^3=3\cdot4x^{3-1}=12x^2\]Simple :)

Answer 10

that's the only thing I understand, all the other rules make no sense though

Answer 11

Well, for now, that's all you're going to need, since you're only tasked to differentiate
\[\Large 3x^{-1}+2-8x^{-\frac12}\]

Answer 12

\[3x ^{-2}+4x\]

Answer 13

Almost... but, why is it 4x?

Answer 14

\[4x ^{-\frac{ 3 }{ 2 }}\] ?

Answer 15

Much better :)

Answer 16

so that's the answer?

Answer 17

with the 3x^(-2), it is

Answer 18

Thank you!

Answer 19

No problem.