anonymous
  • anonymous
find the derivative of f(x)=sqrt (x^2+2x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[f(x)=\sqrt{x^2+2}\]
swissgirl
  • swissgirl
\( f(x)=(x^2+2)^{1 \over 2}\)
anonymous
  • anonymous
thats not one of the choices

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swissgirl
  • swissgirl
noooooooo its easier to solve in this format
anonymous
  • anonymous
huh
anonymous
  • anonymous
anonymous
  • anonymous
\[1\div2\sqrt{x ^{2}+2x}\times(2x+2)\]
swissgirl
  • swissgirl
\( f(x)=(x^2+2)^{1 \over 2}\) is the same as \( f(x)= \sqrt{x^2+2}\)
zepdrix
  • zepdrix
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
anonymous
  • anonymous
i understand but the assignment is keeping it that way so im getting confused thats all
zepdrix
  • zepdrix
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 ^^
zepdrix
  • zepdrix
swiss is typing up a storm :P she prolly got something for you lol
anonymous
  • anonymous
lol
zepdrix
  • zepdrix
she might just be trolling us, it's hard to tell at this point -_- lol
swissgirl
  • swissgirl
\(f(x)=(x^2+2)^{1 \over 2}\) \( {1 \over 2}(x^2+2)^{({1 \over 2}-1)}*2x\) \( {1 \over 2}(x^2+2)^{-1 \over 2}*2x\) \(\large { 1 \over 2\sqrt{x^2+2}}*2x\) \(\large {2x \over 2(x^2+2)}\) \(\large {x \over (x^2+2)}\)
swissgirl
  • swissgirl
okkk i had to post loil but if you are still interested I can explain what i did
zepdrix
  • zepdrix
Woops! Your sqrt disappeared on the last couple steps there! <:o
swissgirl
  • swissgirl
@zepdrix was getting too curious
swissgirl
  • swissgirl
uuugghhhhhhhhhh
zepdrix
  • zepdrix
XD
swissgirl
  • swissgirl
i hate latex it never listens
swissgirl
  • swissgirl
ok one more time at it
anonymous
  • anonymous
:(
anonymous
  • anonymous
ok thanks
anonymous
  • anonymous
you guys rock
zepdrix
  • zepdrix
Do the first 3 steps make sense though sandy? c: those she did correctly.
swissgirl
  • swissgirl
ok lets explain the first 3 steps that last 2 steps are basic simplification neways
anonymous
  • anonymous
u used the power rule first
swissgirl
  • swissgirl
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
swissgirl
  • swissgirl
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
swissgirl
  • swissgirl
Do you follow @sandy524
swissgirl
  • swissgirl
alrighty ill just give you the last two lines that i messed up \( \large {2x \over 2\sqrt{x^2+2}}\) \( \large {x \over \sqrt{x^2+2}}\)
anonymous
  • anonymous
i dont get what this means

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