How do you find the second derivative of $f (x) = 3 x^{- 2}$ $f(x)=3x^-2$ ?

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How do you find the second derivative of $f (x) = 3 x^{- 2}$ $f(x)=3x^-2$ ?

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Answer 1 · 2017-01-30T17:45:08

$\frac{d^{2}}{{d x}^{2}} 3 x^{- 2} = 18 x^{- 4}$ $d^2/(dx^2) 3x^(-2) =18x^-4$

Explanation:

Using the power rule:

$\frac{d}{d x} 3 x^{- 2} = (- 2) \cdot 3 x^{- 2 - 1} = - 6 x^{- 3}$ $d/(dx) 3x^(-2) = (-2)*3x^(-2-1) = -6x^(-3)$

$\frac{d^{2}}{{d x}^{2}} 3 x^{- 2} = \frac{d}{d x} - 6 x^{- 3} = (- 3) \cdot (- 6) x^{- 3 - 1} = 18 x^{- 4}$ $d^2/(dx^2) 3x^(-2) = d/(dx) -6x^-3 = (-3)*(-6)x^(-3-1) =18x^-4$

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How do you find the second derivative of $f (x) = 3 x^{- 2}$ $f(x)=3x^-2$ ?

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