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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= - 1 \cdot x^{- 1 - 1}

Simplify

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

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

\frac{d}{d x} (\frac{sin ^{2} ( x )}{x ^{2}})

\frac{d}{d x} (3^{3 x})

\frac{\partial}{\partial x} (2 e^{x^{9} y})

(\frac{x + 9}{x - 9})^{5}

x \to 16 lim (\frac{( 4 - x )}{( 16 x - x ^{2} )})

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