What is the derivative of $\frac{5}{x^{2}}$ $5/x^2$ ?

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What is the derivative of $\frac{5}{x^{2}}$ $5/x^2$ ?

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Answer 1 · 2016-05-30T13:25:17

$- \frac{10}{x^{3}}$ $-10/x^3$

Explanation:

Begin by expressing $\frac{5}{x^{2}} = 5 x^{- 2}$ $5/x^2=5x^-2$

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

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

$\Rightarrow \frac{d}{d x} (5 x^{- 2}) = (- 2) \times 5 x^{- 2 - 1} = - 10 x^{- 3} = - \frac{10}{x^{3}}$ $rArrd/dx(5x^-2)=(-2)xx5x^(-2-1)=-10x^-3=-10/x^3$

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What is the derivative of $\frac{5}{x^{2}}$ $5/x^2$ ?

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