What is (\partial)/(\partial x)(3/x) ?

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

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(\partial)/(\partial x)(3/x)

\frac{\partial}{\partial x} (\frac{3}{x})

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

Solution steps

\frac{\partial}{\partial x} (\frac{3}{x})

Take the constant out:

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

= 3 \frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

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

= 3 \frac{\partial}{\partial x} (x^{- 1})

Apply the Power Rule:

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

= 3 (- 1 \cdot x^{- 1 - 1})

Simplify

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

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

\frac{d x}{d t} = - 3 x (x^{2} - 1)

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

\frac{d y}{d t} = \frac{t ^{2}}{y ( 2 + t ^{3} )}

\frac{d}{d x} (sin (\frac{π}{2}))

x \to 0 lim (\frac{e ^{x} - 1}{x ^{3}})

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