Question

Differentiate f(x)= (x-6)^2/3 where c=6 using the alternative of the derivative

Answer 1

alternative form: f(x)-f(c)/ x-c as limit of x approaches c

Answer 2

Is the problem\[(x-6)^{2/3}\] or
\[\frac{(x-6)^{2} }{3}\]

Answer 3

oh sorry it's the first one (x-6)^(2/3)

Answer 4

Okay brb working on problem.

Answer 5

lol kk

Answer 6

\[f'(x)= \frac{f(x)-f(c)}{x-c}\]
Where c=6
f(6)=0
so then we have
\[f'(x)= \frac{(x-6)^{2/3}-0}{x-6}\]
or
\[f'(x)= \frac{(x-6)^{2/3}}{x-6}\]

Answer 7

does that come down to 1/ x-6?

Answer 8

Using a different method, the correct answer is
(2/3)(x-6)^(-1/3)
\[\frac{2}{3}(x-6)^{-1/3}\]
I have to go, but I can help you in like ~40 mins if you still have problems

Answer 9

You can't simplify to 1/(x-6) because of the (3/2) power in the numerator.

Answer 10

oh alrite thank you