What is (\partial)/(\partial x)((u^2)/(x^2)) ?

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

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(\partial)/(\partial x)((u^2)/(x^2))

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

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

Solution steps

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

Treat

u

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= u^{2} (- 2 x^{- 2 - 1})

Simplify

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

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

\frac{x d y}{d x} + 3 y = x^{3} - x

y^{^{'}} = 2 y^{2} + x y^{2}, y (0) = 1

\frac{d}{d x} (\frac{1}{5 - 2 x})

\int \frac{9 - 162 x}{64 - 81 x ^{2}} d x

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