What is (\partial)/(\partial x)(x^{-1/2}) ?

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

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(\partial)/(\partial x)(x^{-1/2})

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

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

Solution steps

\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}}}

\int \frac{5}{x ^{2} + 2 x + 5} d x

f (x) = 9 + cot (x) - 2 csc (x), at x = 1

t \to 4 lim (t ∣ t - 4 ∣)

x \to 0 lim (x \frac{π}{2})

\frac{2 x}{x - 1}

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