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  • DLS

DE help

Mathematics
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  • DLS
\[y=\log(x^{2}\sqrt{x^{2}+1})\]
  • DLS
I got something like this \[\frac{1}{x^{2}\sqrt{x^{2}+1}} \times 2\sqrt{x^{2}+1} \times 2x\]
  • DLS

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Other answers:

there is a bit of editing you should have used product rule
for (x^2 sqrt{x^2+1})
  • DLS
how?:o
\[\frac{ d(x^2 \sqrt{x^2+1}) }{ dx }=x^2\frac{ d \sqrt{x^2+1} }{ dx }+\sqrt{x^2+1}*2x\]
  • DLS
woah :o thanks
:) YW
  • DLS
how did you get dx in the denominator?
you are differentiating with respect to x
i can write it as\[\frac{ d }{ dx }(\sqrt{x^2+1}*x^2)\]
  • DLS
oh wait equation is messed up lol just asec
  • DLS
\[\frac{dy}{dx}=\frac{dlog(x^{2}\sqrt{x^{2}+1}}{dx^{2}\sqrt{x^{2}+1}} \times \frac{dx^{2} \sqrt{x^{2}+1}}{d \sqrt{x^{2}+1}} \] ..so on
NO
  • DLS
i do like this,where i didnt diff. wrt. dx
  • DLS
thats how im taught >.>
you have to differentiate wrt x, you can't diffrentiate wrt to function
  • DLS
wth :/ am i taught wrong :S but i was getting all the answers like this
differentiation is done wrt to a variable basically differentiation tells us rate of change of one variable wrt to another and function is something that tells us the relation between those two variables so we can never get rate of change wrt to a function
  • DLS
okay..!
\[\frac{ d }{ dx }(\sqrt{x^2+1})*x^2+2x* \sqrt{x^2+1}\]
  • DLS
okay...clear!
cool :D
\[\frac{ d }{ dx } (\sqrt{x^2+1})=\frac{ 1 }{ \sqrt{x^2+1} }*\frac{ d }{ dx }(x^2+1)\]
there will be a factor of -1/2 multiplied in RHS
  • DLS
derivative of sqrt x is 1/2x right :o
-1/2 x
  • DLS
\[\frac{d \sqrt{x}}{dx}= \frac{1}{2 \sqrt{x}}\] does my coaching class suck lol :/
  • DLS
http://wiki.answers.com/Q/What_is_the_derivative_of_square_root_of_x
no they are right let me show you
  • DLS
will it be like this: \[\frac{1}{2 \sqrt{x^{2}+1}} \times 2x = \frac{x}{\sqrt{x^{2}+1}} \]
\[\frac{ d }{ dx } (x)^{-1/2}= \frac{ -1 }{ 2 }(x)^{-1/2-1}\]
  • DLS
so how do we have 2 answers
no we have one, just be careful in calculating power
  • DLS
okay..
  • DLS
so final answer im getting is
  • DLS
\[\frac{1}{x(x^{2}+1}\]
  • DLS
\[\frac{1}{x^{2} \sqrt{x^{2}+1}} \times \frac{x}{\sqrt{x^{2}+1}}\]
  • DLS
which is wrong :/ http://www.wolframalpha.com/input/?i=derivative+of+log%28x%5E2%28sqrt%28x%5E2%2B1%29%29%29
\[\frac{ d }{ dx } (\sqrt{x^2+1})=\frac{1 }{ 2 }(\sqrt{x^2+1})^{-3/2}* 2x\] your answer
  • DLS
what did you do
\[\frac{ d }{ dx }(x^n)=nx^{n-1}\] hope you know this formula
  • DLS
oh okay!

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