Question

Need Help! Find derivative of f(x)=1-1/2sqrt(1-x)

Answer 1

I'm really confused on how to find the derivative of fraction square root part..do I do the quotient rule?

Answer 2

oh no !!

Answer 3

as much as i lectured before about not using rational exponents, that was when you had
\[\frac{d}{dx}\sqrt{f(x)}\]

Answer 4

\[f(x) = 1-\frac{ 1 }{ 2\sqrt{1-x} }?\]

Answer 5

Yep, that's it astrophysics!

Answer 6

for this one you probably do want to use rational exponents

Answer 7

LOL THANKS SATTELITE!

Answer 8

\[1-\frac{1}{2}(1-x)^{-\frac{1}{2}}\]

Answer 9

ye was gonna do that

Answer 10

then go nuts

Answer 11

i guess you are looking for the second derivative of the previous one right?

Answer 12

wow...so like why couldnt I use the rational exponents for the other question we were doing? and yea

Answer 13

of course you could, what i meant was it is not necessary once you know it
because after you use the power rule, you are going to have to convert out of the rational exponents to do any sort of computation

Answer 14

i wasn't saying you couldn't use it, i was saying you SHOULDN'T use it because you should just memorize the derivative of the square root function or its composition

Answer 15

kk gotcha

Answer 16

this one would be a bear to do without the power rule, but let me lecture once again

Answer 17

Power rule and chain rule

Answer 18

DO NOT USE THE QUOTIENT RULE IF THE NUMERATOR IS A NUMBER !!

Answer 19

^ this, I see so many people applying quotient rule to problems like that

Answer 20

i will pontificate more on that in a moment, lets finish this one

Answer 21

Okay enough about bashing on mwah, let's finish the problem

Answer 22

\[-\frac{1}{4}(1-x)^{-\frac{3}{2}}\] is your derivative right?

Answer 23

Yea and then I solved it down to what I have above

Answer 24

are you trying to set it equal to zero?

Answer 25

yea...should I not

Answer 26

well not you should not
again the curse of rational exponents

Answer 27

\[-\frac{1}{4\sqrt{(1-x)^2}}\]

Answer 28

crap

Answer 29

\[-\frac{1}{4\sqrt{(1-x)^3}}\]

Answer 30

a fraction is only zero if the numerator is

Answer 31

so forget about setting this equal to zero, it is never zero
lesson: once you have the derivative (whatever method) get it out of exponential notation and write what it really is

Answer 32

my guess is you are asked about concavity right?