What is (\partial)/(\partial y)((2x)/(y^3)) ?

The answer to (\partial)/(\partial y)((2x)/(y^3)) is -(6x)/(y^4)

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(\partial)/(\partial y)((2x)/(y^3))

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

- \frac{6 x}{y ^{4}}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= 2 x \frac{\partial}{\partial y} (\frac{1}{y ^{3}})

Apply exponent rule:

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

= 2 x \frac{\partial}{\partial y} (y^{- 3})

Apply the Power Rule:

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

= 2 x (- 3 y^{- 3 - 1})

Simplify

2 x (- 3 y^{- 3 - 1}) : - \frac{6 x}{y ^{4}}

= - \frac{6 x}{y ^{4}}

\frac{d y}{d x} = \frac{y ( ln ( 4 y ) - ln ( 4 x ) + 3 )}{3 x}

t^{\frac{9}{2}}

\int - \frac{1}{512} sin (8 x) d x

x \to - 1 lim (\frac{x ^{3} - x}{x - 1})

x \to 1 lim (ln (3 x) + e^{x})

What is (\partial)/(\partial y)((2x)/(y^3)) ?
The answer to (\partial)/(\partial y)((2x)/(y^3)) is -(6x)/(y^4)