How do you find the second derivative of $y = \frac{1}{x}$ $y=1/x$ ?

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How do you find the second derivative of $y = \frac{1}{x}$ $y=1/x$ ?

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Answer 1 · 2017-01-25T12:00:08

$\frac{d^{2} y}{{d x}^{2}} = \frac{2}{x^{3}}$ $(d^2y)/(dx^2)=2/x^3$

Explanation:

differentiate using the $power rule$ $color(blue)"power rule"$

$color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(ax^n)=nax^(n-1))color(white)(2/2)|)))$

$y=1/x=x^-1$

$rArrdy/dx=-x^-2$

To obtain the second derivative, differentiate $dy/dx$

$rArr(d^2y)/(dx^2)=2x^-3=2/x^3$

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How do you find the second derivative of $y = \frac{1}{x}$ $y=1/x$ ?

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How do you find the second derivative of $y = \frac{1}{x}$ $y=1/x$ ?