Question

find the derivative of f(x)=sqrt (x^2+2x)

Answer 1

\[f(x)=\sqrt{x^2+2}\]

Answer 2

\( f(x)=(x^2+2)^{1 \over 2}\)

Answer 3

thats not one of the choices

Answer 4

noooooooo its easier to solve in this format

Answer 5

huh

Answer 6

#4

Answer 7

\[1\div2\sqrt{x ^{2}+2x}\times(2x+2)\]

Answer 8

\( f(x)=(x^2+2)^{1 \over 2}\) is the same as \( f(x)= \sqrt{x^2+2}\)

Answer 9

Sandy, it's easier to differentiate a root if you rewrite it as a fractional exponent :)
She was just rewriting the problem a little nicer for you, not the solution. :D

Answer 10

i understand but the assignment is keeping it that way so im getting confused thats all

Answer 11

it might be a good idea to switch to a fractional exponent, do the differentiation, then as your last step, put whatever fractional exponent you have back into root form.
UNLESS you remember the derivative of sqrt(x), then you skip doing that step ^^

Answer 12

swiss is typing up a storm :P she prolly got something for you lol

Answer 13

lol

Answer 14

she might just be trolling us, it's hard to tell at this point -_- lol

Answer 15

\(f(x)=(x^2+2)^{1 \over 2}\)

\( {1 \over 2}(x^2+2)^{({1 \over 2}-1)}*2x\)
\( {1 \over 2}(x^2+2)^{-1 \over 2}*2x\)

\(\large { 1 \over 2\sqrt{x^2+2}}*2x\)

\(\large {2x \over 2(x^2+2)}\)

\(\large {x \over (x^2+2)}\)

Answer 16

okkk i had to post loil but if you are still interested I can explain what i did

Answer 17

Woops! Your sqrt disappeared on the last couple steps there! <:o

Answer 18

@zepdrix was getting too curious

Answer 19

uuugghhhhhhhhhh

Answer 20

XD

Answer 21

i hate latex it never listens

Answer 22

ok one more time at it

Answer 23

:(

Answer 24

ok thanks

Answer 25

you guys rock

Answer 26

Do the first 3 steps make sense though sandy? c: those she did correctly.

Answer 27

ok lets explain the first 3 steps that last 2 steps are basic simplification neways

Answer 28

u used the power rule first

Answer 29

I used the chain rule by first bringing down the exponent in front of the bracket and then subtracting one from the exponent as you can see and then I derived what was in the bracket. The derivative of x^2+2 is 2x

Answer 30

Well as we see there are 2 things that need to be derived. The outer exponent and the inner exponent. So the chain rule states that you first derive the outer part and then you derive what is in the bracket

Answer 31

Do you follow @sandy524

Answer 32

alrighty ill just give you the last two lines that i messed up

\( \large {2x \over 2\sqrt{x^2+2}}\)

\( \large {x \over \sqrt{x^2+2}}\)

Answer 33

i dont get what this means