What is (\partial}{\partial x}(\frac{v^2)/x) ?

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

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(\partial}{\partial x}(\frac{v^2)/x)

\frac{\partial}{\partial x} (\frac{v ^{2}}{x})

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

Solution steps

\frac{\partial}{\partial x} (\frac{v ^{2}}{x})

Treat

v

as a constant

Take the constant out:

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

= v^{2} \frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

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

= v^{2} \frac{\partial}{\partial x} (x^{- 1})

Apply the Power Rule:

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

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

Simplify

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

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

\int - ln (x) e^{- x} d x

f (x) = 4 x e^{x}, at x = 0

\int \frac{x ^{5} - x ^{4} + 4 x ^{3} - 4 x ^{2} + 8 x - 4}{( x ^{2} + 2 ) ^{3}} d x

- \frac{6 x}{( x ^{2} - 4 ) ^{2}}

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

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