Final Answer
$\frac{-\frac{3}{2}}{\sqrt{x^{5}}}$
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Step-by-step Solution
Problem to solve:
$\frac{d}{dx}\left(x^{-1\cdot \frac{3}{2}}\right)$
Choose the solving method
1
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
$-\frac{3}{2}x^{-\frac{5}{2}}$
2
Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number
$\frac{-\frac{3}{2}}{\sqrt{x^{5}}}$
Final Answer
$\frac{-\frac{3}{2}}{\sqrt{x^{5}}}$