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

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

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(\partial)/(\partial x)(v/x)

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

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

Solution steps

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

Treat

v

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{d}{d x} (\frac{x - 2}{x ^{2} - 2 x + 4})

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

\int x 5^{x^{2}} d x

\frac{d}{d x} (2 x^{3} - 3 x^{2} - 5)

f (x) = 5 cos^{2} (x)

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