Question

((9-x^2)^2)^(1/3) use the chain rule to find the derivative. Can it also be written like this: (9−x^2)2/3?

Answer 1

hold on almost got it

Answer 2

thanks!

Answer 3

(4x^3-36x) (x^4-18x^2+81)^(-2/3)
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3

Answer 4

how did you do that?

Answer 5

haha it's a bit involved but i got ya

Answer 6

just the first step is fine :)

Answer 7

or the first two or 3 :)

Answer 8

what i first did was did the FOIL method for (9-x^2)^2 so that we didn't have power to a power to a power thing and that came out to be
x^4-18x^2+81

Answer 9

so then you got this (x^4-18x^2+81)^(1/3)

Answer 10

did you use the chain rule?

Answer 11

not yet

Answer 12

then you chunk the whole thing as a variable and deferenciate like normal.

so we bring down the (1/3) and put that as a coeffiecent in the front and then re write the whoel thing and then subtract one from the power, just like a normal thing

Answer 13

but since you did multiple variables at the same time, you have to use the chain rule

Answer 14

and that involves you taking the derivative of the chunk that we just deferenciated

so that was

(1/3) (x^4-18x^2+81)^(-2/3) *applying chain rule* (4x^3-36x)

so then you get this

(1/3) (4x^3-36x) (x^4-18x^2+81)^(-2/3)

Answer 15

and you're done

Answer 16

thank you, something that has always confused me is negative exponents, for example, (9x+8)^(-2/3) how would you write that?

Answer 17

ahh yeah it's not bad. A negative exponet means 1/(that thing)

so for example

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

Answer 18

but when it' a fraction like that you alwasy have to remember (power/root)

so if we had

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

Answer 19

opps i meant
x(3/2) = 1/(SQRT(x^3))

Answer 20

Watch a few videos from this guy. He's really good and does a ton of examples
http://www.youtube.com/watch?v=6kScLENCXLg

Answer 21

thank you for all your help!

Answer 22

no problem