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Derivative of $$$\frac{1}{\sqrt{x}}$$$
The calculator will find the derivative of $$$\frac{1}{\sqrt{x}}$$$, with steps shown.
Related calculator: Derivative Calculator
Solution
Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = - \frac{1}{2}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\frac{1}{\sqrt{x}}\right)\right)} = {\color{red}\left(- \frac{1}{2 x^{\frac{3}{2}}}\right)}$$Thus, $$$\frac{d}{dx} \left(\frac{1}{\sqrt{x}}\right) = - \frac{1}{2 x^{\frac{3}{2}}}$$$.
Answer
$$$\frac{d}{dx} \left(\frac{1}{\sqrt{x}}\right) = - \frac{1}{2 x^{\frac{3}{2}}}$$$A