Question

(x^2/3)*((6-x)1/3)
I'm suppose to find the derivative, but I'm getting a different answer than the book
HELP

Answer 1

Is it this?\[f(x)=\frac{ x ^{2} }{ 3 }*(\frac{ 6-x }{ 3 })\]

Answer 2

It's kind of confusing the way you typed it up there.

Answer 3

no x to the 2/3 power times 6-x to the 1/3 power

Answer 4

Got it! Let me work on it for a tiny bit...

Answer 5

thanks

Answer 6

Might sound crazy but I did some simplifying and get the function down to\[f(x)=(6x ^{2}-x ^{3})^{\frac{ 1 }{ 3 }}\]

Answer 7

let me try real quick

Answer 8

I get this crazy thing...but I gave it a fightin' try...

Answer 9

\[f'(x)=\frac{ 4-x }{ x(6-x)^{\frac{ 2 }{ 3 }} }\]

Answer 10

yep thats it

Answer 11

Sorry in advance for being so so so....right?

Answer 12

can i walk you through what i did
and you can tell me what i did wrong

Answer 13

Are you kidding me?!

Answer 14

As crazy as that looks and it's right?

Answer 15

ya it sure is lol

Answer 16

Lol is right!

Answer 17

Ok then...I guess just simplify it first and then it's so much easier...even I could get it!

Answer 18

first i derived the equation without combining. so it was.....

Answer 19

it was a mess is what it was! I tried it with a multiple chain rule and it was a disaster!

Answer 20

\[x^{2/3}*(6-x)^{1/3}p r i m e +(6-x)^{1/3}*x ^{2/3}p r i m e\]

Answer 21

so then

Answer 22

The trick here was to convert the \[(x)^{\frac{ 2 }{ 3 }}\]into\[(x ^{2})^{\frac{ 1 }{ 3 }}\]that way they both had the same index and could be multiplied out to\[(6x ^{2}-x ^{3})^{\frac{ 1 }{ 3 }}\]See? So much easier!

Answer 23

Yeah, right...easier my butt...

Answer 24

cool thank you!

Answer 25

Wow! You are so welcome! Getting that correct just made my day! TY for the medal, also!

Answer 26

is that a joint or a whistle in your mouth in your profile pic? ; )

Answer 27

black and mild
might as well be a joint or a blunt though