Question

Find f'(a) for the function f(x) = {5}/{\sqrt{1-x}}.

Answer 1

i got -5/2a^(-1/2)/(sqrt(1-a))^2
but it says it's wrong

Answer 2

\[\Large f(x)\quad=\quad \frac{5}{(1-x)^{1/2}}\]

\[\Large f'(x)\quad=\quad -\frac{1}{2}\cdot\frac{5}{(1-x)^{3/2}}(1-x)'\]
\[\Large f'(x)\quad=\quad \frac{1}{2}\cdot \frac{1}{(1-x)^{3/2}}\]

Answer 3

Hmm I'm not sure where your a in the numerator came from.

Answer 4

Oh :p u did something fancy, lemme simplify this a little further.

Answer 5

Woops my 5 disappeared in the last step of my previous post.
\[\Large f'(a)\quad=\quad \frac{5/2}{(1-a)^{3/2}}\]

Answer 6

Ya I can't seem to figure out what's going on with your solution..
Did you do quotient rule or something?

Answer 7

yes i used a quotient rule to find it

Answer 8

Seems a bit easier to just simplify it down and apply power rule.\[\Large f(x)\quad=\quad 5(1-x)^{-1/2}\]

Answer 9

lot of places to make mistakes going the quotient route :[

Answer 10

Remember how to write roots as rational expressions?\[\Large \frac{1}{\sqrt x} \quad=\quad \frac{1}{x^{1/2}}\quad=\quad x^{-1/2}\]

Answer 11

i just learned about quotient rule today, it worked for the other proble i had one but for this one it didn't

Answer 12

We can try quotient rule if u want. it's a bit messy but here we go!! :)

Answer 13

\[\Large f(x)\quad=\quad \frac{5}{\sqrt{1-x}}\]
\[\Large f'(x)\quad=\quad \frac{\color{royalblue}{(5)'}(\sqrt{1-x})-(5)\color{royalblue}{(\sqrt{1-x})'}}{(\sqrt{1-x})^2}\]

Answer 14

So there is our setup, we need to take the derivative of the blue parts.
Make sense so far?

Answer 15

the 5 will be 0 and the sqrt(1-x) would be -1 right

Answer 16

http://www.wolframalpha.com/input/?i=derivative+5%281-x%29^%28-1%2F2%29

Answer 17

Remember the derivative of sqrtx? It's a good one to have memorized cause it comes up so often.\[\Large (\sqrt x)' \quad=\quad \frac{1}{2\sqrt x}\]

Answer 18

I got a little worried when you said that the `sqrt(1-x) would be -1`.
So I just wanna make sure you understand sqrt derivative.

Answer 19

So derivative of sqrt(1-x) would give us,\[\Large \frac{1}{2\sqrt{1-x}}(1-x)'\]

Answer 20

Good ole chain rule :U

Answer 21

oh yeah, since it is squared it should be 1^1/2 - X^1/2 which will give me -1/2x^-1/2 right?

Answer 22

? D: hmm