Find the derivative d/dx(x^(-3)) using the power rule

 Exercise

$\frac{d}{dx}x^{-3}$

 

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$-3x^{\left(-3-1\right)}$

 

Subtract the values $-3$ and $-1$

$-3x^{-4}$

 

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$-3\left(\frac{1}{x^{\left|-4\right|}}\right)$

 

Multiplying the fraction by $-3$

$\frac{-3}{x^{\left|-4\right|}}$

$\frac{-3}{x^{\left|-4\right|}}$

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