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MTALHAHASSAN2
 one year ago
Determine the second derivative of each of the follwoing:
MTALHAHASSAN2
 one year ago
Determine the second derivative of each of the follwoing:

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thomas5267
 one year ago
Best ResponseYou've already chosen the best response.0\[ \sqrt{x}=x^{1/2} \]

MTALHAHASSAN2
 one year ago
Best ResponseYou've already chosen the best response.0but know what about the second derivative

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1what is your starting equation?

MTALHAHASSAN2
 one year ago
Best ResponseYou've already chosen the best response.0wait but how are we goona get the second derivative

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1we are going to apply the power rule again.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1We apply the power rule twice, that is all. (Want an example?)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Ok, just tell me what do you get for the derivative of \(x^{1/2}\), when you apply the power rule?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Yeah, 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
 one year ago
Best ResponseYou've already chosen the best response.1The first derivative of \(\large\color{black}{ \displaystyle x^n }\) is given by the power rule: \(\large\color{black}{ \displaystyle \frac{d}{dx}\left[x^n\right]=nx^{n1} }\) and then the second derivative of that would be: \(\large\color{black}{ \displaystyle \frac{d^2}{dx^2}\left[x^n\right]=\frac{d}{dx}\left[nx^{n1}\right]=n(n1)x^{n2} }\) 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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