How do you find the derivative of $f (x) = - \frac{9}{x}$ $f(x)=-9/x$ ?

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How do you find the derivative of $f (x) = - \frac{9}{x}$ $f(x)=-9/x$ ?

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Answer 1 · 2016-05-30T12:57:02

$\frac{9}{x^{2}}$ $9/x^2$

Explanation:

Begin by writing f(x) $= - \frac{9}{x} = - 9 x^{- 1}$ $=-9/x=-9x^-1$

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

$\frac{d}{d x} (a x^{n}) = n a x^{n - 1}$ $d/dx(ax^n)=nax^(n-1)$

$\Rightarrow \frac{d}{d x} (- 9 x^{- 1}) = (- 1) \times (- 9) x^{- 1 - 1} = 9 x^{- 2} = \frac{9}{x^{2}}$ $rArrd/dx(-9x^-1)=(-1)xx(-9)x^(-1-1)=9x^-2=9/x^2$

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How do you find the derivative of $f (x) = - \frac{9}{x}$ $f(x)=-9/x$ ?

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How do you find the derivative of $f (x) = - \frac{9}{x}$ $f(x)=-9/x$ ?