What is (\partial)/(\partial x)(1/(sqrt(x))) ?

The answer to (\partial)/(\partial x)(1/(sqrt(x))) is -1/(2x^{3/2)}

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(\partial)/(\partial x)(1/(sqrt(x)))

\frac{\partial}{\partial x} (\frac{1}{x})

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

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{\partial}{\partial 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 (\partial)/(\partial x)(1/(sqrt(x))) ?
The answer to (\partial)/(\partial x)(1/(sqrt(x))) is -1/(2x^{3/2)}