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

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

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

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{d}{d t} (k t e^{3 t})

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

\frac{d ^{2}}{d x ^{2}} (\frac{3}{4 x ^{6}})

\int sin (a x) cos (b x) d x

x \to c lim (m x + b)

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