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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int 1 + \frac{1}{( x + 1 ) ^{2}} d x

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

\int sec^{2} (X) d X

x \to - 3 - lim (\frac{3}{x ^{2} - 9})

\int (3 e^{x} + 5 sin (x)) d x

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