What is (\partial)/(\partial x)((4pi^2y)/(x^2)) ?

The answer to (\partial)/(\partial x)((4pi^2y)/(x^2)) is -(8pi^2y)/(x^3)

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(\partial)/(\partial x)((4pi^2y)/(x^2))

\frac{\partial}{\partial x} (\frac{4 π ^{2} y}{x ^{2}})

- \frac{8 π ^{2} y}{x ^{3}}

Solution steps

\frac{\partial}{\partial x} (\frac{4 π ^{2} y}{x ^{2}})

Treat

y

as a constant

Take the constant out:

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

= 4 π^{2} y \frac{\partial}{\partial x} (\frac{1}{x ^{2}})

Apply exponent rule:

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

= 4 π^{2} y \frac{\partial}{\partial x} (x^{- 2})

Apply the Power Rule:

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

= 4 π^{2} y (- 2 x^{- 2 - 1})

Simplify

4 π^{2} y (- 2 x^{- 2 - 1}) : - \frac{8 π ^{2} y}{x ^{3}}

= - \frac{8 π ^{2} y}{x ^{3}}

What is (\partial)/(\partial x)((4pi^2y)/(x^2)) ?
The answer to (\partial)/(\partial x)((4pi^2y)/(x^2)) is -(8pi^2y)/(x^3)