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

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

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

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

- \frac{8 π ^{2} y}{x ^{3}}

Solution steps

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

arctan (2 x)

x \to 0 lim (\frac{2 x}{0})

e^{x}, x, 0, 2

x \to - 4 lim (- \frac{8}{x ^{2} + 8 x + 16})

x \to 0 lim ((1 - 5 x)^{\frac{4}{x}})

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