What is the derivative of (x^{-1/2}) ?

The derivative of (x^{-1/2}) is -1/(2x^{3/2)}

What is the first derivative of (x^{-1/2}) ?

The first derivative of (x^{-1/2}) is -1/(2x^{3/2)}

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\frac{d}{d x} ((x)^{- \frac{1}{2}})

- \frac{1}{2 x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} ((x)^{- \frac{1}{2}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - \frac{1}{2} x^{- \frac{1}{2} - 1}

Simplify

- \frac{1}{2} x^{- \frac{1}{2} - 1} : - \frac{1}{2 x ^{\frac{3}{2}}}

= - \frac{1}{2 x ^{\frac{3}{2}}}

What is the derivative of (x^{-1/2}) ?
The derivative of (x^{-1/2}) is -1/(2x^{3/2)}
What is the first derivative of (x^{-1/2}) ?
The first derivative of (x^{-1/2}) is -1/(2x^{3/2)}