Question

quotient rule derivative

Answer 1

Easier to simplify first.
=1+8/(3x^(1/3))
=8/3*(-1/3)x^(-2/3)

Answer 2

@amistre64

Answer 3

Should clarify that d/dx (1+8/(3x^(1/3)) is the simplified form which yields 8/3*(-1/3)x^(-2/3) as your derivative

Answer 4

@nukka that is not the correct answer...where did you get the 8/3 are you sure you did derivative?

Answer 5

\[\left(6x ^{2}+16x ^{1/2} \right)\div \left( 6x ^{2} \right)\]
6x^2/6x^2 =1
16x^0.5/6x^2=(8/3)*(1/x^1.5)
d(1+(8/3)*(1/x^1.5))/dx =0+(8/3)*(3/2)x^(1/2)
=\[4\sqrt{x}\]

I guess it turns out differently when i write it down.

Answer 6

Looks like I missed a - in there.
Should be -4sqrtx

Answer 7

@Directrix

Answer 8

wait you are not allowed to?@Directrix

Answer 9

since this is division the only derivative rule we can follow is quotient right?

Answer 10

@Directrix

Answer 11

I am confused by the instruction "quotient rule derivative" and then the instructions on the attachment. So, I'm asking you if you are allowed to use the quotient rule to find the derivative of this function.

Answer 12

in unsimplified form it comes out like this
[(6x^2+a6x^1/2)12x-6x^2*{12x+8/x^1/2}]/(6x^2)^2

Answer 13

sorry a typo 1 will be in place of a

Answer 14

\[\frac{6x^2+16x^{1/2}}{6x^2}\]
\[\frac{6x^2}{6x^2}+\frac{16x^{1/2}}{6x^2}\]
\[1+\frac{8x^{1/2-2}}{3}\]
\[1+\frac{8}{3}x^{-3/2}\]then take the derivative

Answer 15

oh wow thank you i ended up doing it last night after like 12 trys i got \[-144x^(3/2)/36x^4\]

Answer 16

\[(1+\frac{8}{3}x^{-3/2})'\to~x-\frac{24}{6}x^{-5/2}\]
\[x-4x^{-5/2}\]
\[\frac{x^{7/2}-4}{x^{5/2}}\]
is what i end up with at best

Answer 17

lol, 1 to 0, not x :) i integrated that one for some reason

Answer 18

\[-\frac{4}{x^{5/2}}\]

Answer 19

when i typed my answer in the hw i got it correct