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}}

x \to 0 lim (\frac{10}{x})

\int_{l n (9)}^{l n (36)} e^{\frac{x}{2}} d x

f (x) = \frac{3}{x ^{4}}

\int e^{x^{2} - 4} d x

x \to 4 lim (3 - 4)

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