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

Question

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Okay brb working on problem.

anonymous · Answer

lol kk

anonymous · Answer

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

anonymous · Answer

does that come down to 1/ x-6?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

oh alrite thank you