What is (\partial)/(\partial x)((5y)/(x^3)) ?

The answer to (\partial)/(\partial x)((5y)/(x^3)) is -(15y)/(x^4)

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(\partial)/(\partial x)((5y)/(x^3))

\frac{\partial}{\partial x} (\frac{5 y}{x ^{3}})

- \frac{15 y}{x ^{4}}

Solution steps

\frac{\partial}{\partial x} (\frac{5 y}{x ^{3}})

Treat

y

as a constant

Take the constant out:

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

= 5 y \frac{\partial}{\partial x} (\frac{1}{x ^{3}})

Apply exponent rule:

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

= 5 y \frac{\partial}{\partial x} (x^{- 3})

Apply the Power Rule:

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

= 5 y (- 3 x^{- 3 - 1})

Simplify

5 y (- 3 x^{- 3 - 1}) : - \frac{15 y}{x ^{4}}

= - \frac{15 y}{x ^{4}}

y^{^{''}} - 9 y^{^{'}} + 18 y = 5 sin (4 t), y (0) = 5, y^{^{'}} (0) = 2

x e^{- 3 x}

\int e^{x} 81 - e^{2 x} d x

y^{^{'}} - y = 3 t e^{2 t}

\frac{\partial}{\partial x} (3 x + 2 y)

What is (\partial)/(\partial x)((5y)/(x^3)) ?
The answer to (\partial)/(\partial x)((5y)/(x^3)) is -(15y)/(x^4)