[MOVED] derivative of ( 4 x^(2/3) ) / x

[kpx001]

basiclly i have (4x^(3/2))/x and im looking for the derrivative.

i can do it when i simplify to 4x^(1/2) but im confused with this algebra. im doing power rule and get 6x^(1/2) *(x)^-1 + 4x^(3/2) * -1 and cant get rid of 4x^3/2.

i get 6 - 4*sqroot(x^3) / sqroot(x) when the answer is 2/sqroot(x)

 

[stapel]

Unfortunately, it is not possible to find any errors when we can't see your work.

Please reply showing all of your steps. Thank you!

Eliz.
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Reason for edit: Must. Learn. To. Spell.

 

[kpx001]

k
y= 4x^(3/2)/x = 4x^(3/2) * (x)^-1

y' = 6x^(1/2) * (x)^-1 + 4x^(3/2) * -1

= 6x^(-1/2) - 4x^(3/2)

= 6 - 4x^(3/2) / sqroot(x)

this is the way id like to know but i figured an easier way

rewrite = 4x^1/2
y' = 2x^(-1/2) = 2/sqroot(x)

 

[stapel]

First, it might help to note the following:

. . . . .x^3/2/x = x^3/2/x^2/2 = x^{3/2 - 2/2} = x^1/2

So you're actually being asked to differentiate 4x^1/2 (except for x = 0, where the original function has a removeable discontinuity).

Meanwhile, how did you get "6x^(1/2) * (x)^-1 + 4x^(3/2) * -1"? In particular, how did you get simply "-1" for the derivative of "x^-1"? What happened to the variable?

Make that correction, and you should be able to get the desired result. :wink:

Eliz.