MTALHAHASSAN2
  • MTALHAHASSAN2
Determine the second derivative of each of the follwoing:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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MTALHAHASSAN2
  • MTALHAHASSAN2
f(x)=sqrt x
MTALHAHASSAN2
  • MTALHAHASSAN2
f1(x)=x^1/2
thomas5267
  • thomas5267
\[ \sqrt{x}=x^{1/2} \]

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MTALHAHASSAN2
  • MTALHAHASSAN2
i know
MTALHAHASSAN2
  • MTALHAHASSAN2
but know what about the second derivative
MTALHAHASSAN2
  • MTALHAHASSAN2
@IrishBoy123
IrishBoy123
  • IrishBoy123
what is your starting equation?
MTALHAHASSAN2
  • MTALHAHASSAN2
f(x)= sqrt x
MTALHAHASSAN2
  • MTALHAHASSAN2
@SolomonZelman
MTALHAHASSAN2
  • MTALHAHASSAN2
wait but how are we goona get the second derivative
SolomonZelman
  • SolomonZelman
we are going to apply the power rule again.
SolomonZelman
  • SolomonZelman
We apply the power rule twice, that is all. (Want an example?)
MTALHAHASSAN2
  • MTALHAHASSAN2
yeah
SolomonZelman
  • SolomonZelman
Ok, just tell me what do you get for the derivative of \(x^{1/2}\), when you apply the power rule?
MTALHAHASSAN2
  • MTALHAHASSAN2
i goted it
SolomonZelman
  • SolomonZelman
Yeah, IrishBoy, lol. I indeed made the biggest mistake in the world. 9I guess the integration power rule got me mixed up just a bit)
SolomonZelman
  • SolomonZelman
The first derivative of \(\large\color{black}{ \displaystyle x^n }\) is given by the power rule: \(\large\color{black}{ \displaystyle \frac{d}{dx}\left[x^n\right]=nx^{n-1} }\) and then the second derivative of that would be: \(\large\color{black}{ \displaystyle \frac{d^2}{dx^2}\left[x^n\right]=\frac{d}{dx}\left[nx^{n-1}\right]=n(n-1)x^{n-2} }\) perhaps there are a few exceptions to this rule: \(n\ne 1\) and \(n\ne 0\) *++++++++++++++++++++++++++++++* \(\Large\color{black}{ \displaystyle f(x)=x^{\frac{1}{5}} }\) the first derivative, using the power rule is as follows: \(\Large\color{black}{ \displaystyle f'(x)=\left(\frac{1}{5}\right)x^{\frac{1}{5}-1} =\frac{1}{5}x^{-\frac{4}{5}}}\) Then, the second derivative you would find by differentiating f'(x) again, using the power rule. \(\Large\color{black}{ \displaystyle f''(x)=\left(\frac{1}{5}\right)\left(-\frac{4}{5}\right)x^{-\frac{4}{5}-1}}\) and this simplifies to: \(\Large\color{black}{ \displaystyle f''(x)=-\frac{4}{5}x^{-\frac{9}{5}}}\)

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