Question

I have the answer can someone just check me please.
Which of the following is f '(x) for f(x)=8 square root x

Answer 1

\[f(x) = 8\sqrt{x} = 8x^{1/2}\]
What's your answer?

Answer 2

I got 4x^(1/2)

Answer 3

Remember what I said earlier?

Answer 4

would it be instead 4x^(-1/2)

Answer 5

no no no I mean just figured it out I think -4x^(1/2)

Answer 6

\[\frac{d}{du}[u^n] = nu^{n-1}\]

Answer 7

Take your existing expression, multiply it by the value of the exponent, and subtract one from the exponent.

Answer 8

right so don't you get 4x^(-1/2)

Answer 9

Yes. But you changed your mind immediately...

Answer 10

because I was still doing the math and I forgot what you said agian as I was doing it and added the 1 again instead of subtracting it.

Answer 11

Here's another one for you:

\[f(x) = x^{2/3}\]

Answer 12

x^(-1/3)

Answer 13

is that right

Answer 14

"Take your existing expression, multiply it by the value of the exponent, and subtract one from the exponent."

Did you do all of that correctly?

Answer 15

yes and I got x^(1/3)

Answer 16

Really. 1 * 2/3 = 1?

Answer 17

oh so then (2/3)x^(1/3)

Answer 18

Better, but still incorrect. 2/3 - 1 = 1/3?

Answer 19

sorry I forgot the (-1/3)

Answer 20

So, final, correct answer is?

Answer 21

(2/3)x^(-1/3)

Answer 22

and written as a fraction with positive exponents that would be?

Answer 23

\[\frac{ 2 }{ 3 }x ^{-1/3}\]

Answer 24

Is "-1/3" a positive exponent?

Answer 25

how do you make it positive exponent?

Answer 26

\[a^{-n} = \frac{1}{a^n}\]

Answer 27

\[\frac{ 2 }{ 3 }x ^{\frac{ 1 }{ 1/3 }}\]

Answer 28

No. \[\frac{2}{3}x^{-1/3} = \frac{2}{3}*x^{-1/3} = \frac{2}{3}*\frac{1}{x^{1/3}} = \frac{2}{3x^{1/3}}\]

Answer 29

oh ok.

Answer 30

To convert an exponential from positive to negative or vice versa, change the sign of the exponent and take the reciprocal.

Answer 31

ok thanks

Answer 32

The answer might also be written as \[\frac{2}{3\sqrt[3]{x}}\] because \[x^{1/n} = \sqrt[n]{x}\]