How do you find the derivative of $g (x) = \frac{1}{\sqrt{x}}$ $g(x)=1/sqrtx$ ?

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How do you find the derivative of $g (x) = \frac{1}{\sqrt{x}}$ $g(x)=1/sqrtx$ ?

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Answer 1 · 2017-08-23T14:55:18

see below

Explanation:

$g (x) = \frac{1}{\sqrt{x}}$ $g(x)=1/sqrtx$

$\Rightarrow \frac{d}{d x} g (x) = \frac{d}{d x} {(x)}^{- \frac{1}{2}}$ $=>d/dxg(x)=d/dx(x)^(-1/2)$

Utilize the formula,

$\frac{d}{d x} x^{n} = n x^{n - 1}$ $d/dxx^n=nx^(n-1)$

$\Rightarrow \frac{d}{d x} {(x)}^{- \frac{1}{2}} = - \frac{1}{2} x^{(- \frac{1}{2} - 1)} = - \frac{1}{2 x \sqrt{x}}$ $=>d/dx(x)^(-1/2)=-1/2x^((-1/2-1))=-1/(2xsqrtx)$

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How do you find the derivative of $g (x) = \frac{1}{\sqrt{x}}$ $g(x)=1/sqrtx$ ?

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