Question

if f(x)=8sqrtx, find f'(x) and f"(x)
if f(x)=3rd root of sqrtx^4, find f'(x) and f"(x)
help :(

Answer 1

\[\Large\rm f(x)=8\sqrt x\]\[\Large\rm f(x)=8x^{1/2}\]Ok with that step?

Answer 2

Rewriting a root as a rational exponent allows you to easily apply your power rule.

Answer 3

zepdrix you got this one?

Answer 4

mhm

Answer 5

yes I understand that step

Answer 6

So what do you get for your first derivative? :)\[\Large\rm f'(x)=8\cdot\frac{1}{2}x^{\frac{1}{2}-1}\]Something like that, yah?
Understand how to simplify the exponent?

Answer 7

is it -4x^1/2 ?

Answer 8

oops i mean to the -1/2

Answer 9

okay so f'(x)=4x^-1/2 & f"(x)=-2x^-3/2 ?

Answer 10

Mmm yes good! :)

Answer 11

Next one will follow the same process, power rule and such.
We just need to get it into the proper rationalize exponent form.\[\Large\rm f(x)=\sqrt[3]{x^4}\]

Answer 12

The degree of the root becomes the denominator.
In our last question, we had a `square root`, which is a `2nd root`.
That's why we had a 2 on the bottom of our fraction.

Answer 13

okay so f'(x) will be 4/3x^1/3?

Answer 14

good c:

Answer 15

thanks :) & f"(x)=4/9x^-2/3

Answer 16

yay good job \c:/

Answer 17

lol thank you :) I just needed some reassurance. I appreciate your help :)