Question

If f(x)=sqrt of (4sinx+2) then f'(0)=

Answer 1

\[f(x)=\sqrt{4\sin (x)+2}?\]

Answer 2

If so, chain rule.

Answer 3

use
\[\frac{d}{dx}\sqrt{f(x)}=\frac{f'(x)}{2\sqrt{f(x)}}\]

Answer 4

@satellite73 has been nice enough to be more specific than I am.

Answer 5

\[\prime(x)=4cosx?\]

Answer 6

i feel like i did something wrong though becuz my answer is different than the choices given

Answer 7

@Limitless only because although this is clearly a "chain rule' problem you can prove what i wrote above directly in a couple short lines without appealing to the chain rule.
likewise for \((f^2)^{'}=2ff'\)

Answer 8

@monkeywall101 did you understand what i wrote above?

Answer 9

@satellite73, you appealed to implicit differentiation, didn't you? (I'm honestly not sure.) Either way, your approach is interesting.

Answer 10

not really, how come the t is still the power of f?

Answer 11

it is identical to the "proof" that \(\frac{d}{dx}\sqrt{x}=\frac{1}{2\sqrt{x}}\) rationalize the numerator and you get the expression for the derivative times \(\frac{1}{2\sqrt{f}}\)

Answer 12

@monkeywall101 do you know the derivative of \(\sqrt{x}\) ?

Answer 13

\[\prime'(x)=4cosx \div2\sqrt{4sinx+2}\]

Answer 14

yes, although you might want to cancel a 2 top and bottom

Answer 15

get \(f'(x)=\frac{2\cos(x)}{\sqrt{4\sin(x)+2}}\)

Answer 16

then you can compute \(f'(0)\) right?

Answer 17

yes i got that, but when i put in 0 into all the x's the answer is not the same as the choices

Answer 18

what do you get when you replace \(x\) by 0 ?

Answer 19

\[2/\sqrt{2}\]

Answer 20

true, but what is another simpler form of this number? hint: rationalize the denominator

Answer 21

oh!!!

Answer 22

omg i feel so stupid now

Answer 23

in fact, why don't we do this in a more general setting
\[\frac{a}{\sqrt{a}}=\frac{a}{\sqrt{a}}\times \frac{\sqrt{a}}{\sqrt{a}}=\frac{a\sqrt{a}}{a}=\sqrt{a}\]

Answer 24

now you will never forget it right?

Answer 25

of course of course!! thanks so much! u were great help!! :)

Answer 26

yw

Answer 27

so smart thank you!! :)