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

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

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(\partial)/(\partial x)(r/x)

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

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

Solution steps

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

Treat

r

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int \frac{1}{x ^{2} 64 x ^{2} + 81} d x

\frac{d y}{d x} = \frac{( x - 1 )}{y - 4}

y = \frac{1}{2} x + 8

f^{^{'}} (x) = x

\frac{d}{d x} (ln (- e^{- x} + e + 1))

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