What is (\partial)/(\partial x)(1/(2sqrt(x))) ?

The answer to (\partial)/(\partial x)(1/(2sqrt(x))) is -1/(4x^{3/2)}

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(\partial)/(\partial x)(1/(2sqrt(x)))

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

- \frac{1}{4 x ^{\frac{3}{2}}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

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

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

Simplify

\frac{1}{2} (- \frac{1}{2} x^{- \frac{1}{2} - 1}) : - \frac{1}{4 x ^{\frac{3}{2}}}

= - \frac{1}{4 x ^{\frac{3}{2}}}

x \to 8 lim (- (2 x - 8))

\int (7 x^{2} - 8 x) e^{2 x} d x

y^{^{'}} = \frac{- y}{x}

\frac{d}{d x} (\frac{x}{6 + x})

\frac{\partial}{\partial x} (\frac{1}{2 + x y ^{2}})

What is (\partial)/(\partial x)(1/(2sqrt(x))) ?
The answer to (\partial)/(\partial x)(1/(2sqrt(x))) is -1/(4x^{3/2)}