What is (\partial)/(\partial x)((4y)/(x^5)) ?

The answer to (\partial)/(\partial x)((4y)/(x^5)) is -(20y)/(x^6)

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(\partial)/(\partial x)((4y)/(x^5))

\frac{\partial}{\partial x} (\frac{4 y}{x ^{5}})

- \frac{20 y}{x ^{6}}

Solution steps

\frac{\partial}{\partial x} (\frac{4 y}{x ^{5}})

Treat

y

as a constant

Take the constant out:

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

= 4 y \frac{\partial}{\partial x} (\frac{1}{x ^{5}})

Apply exponent rule:

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

= 4 y \frac{\partial}{\partial x} (x^{- 5})

Apply the Power Rule:

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

= 4 y (- 5 x^{- 5 - 1})

Simplify

4 y (- 5 x^{- 5 - 1}) : - \frac{20 y}{x ^{6}}

= - \frac{20 y}{x ^{6}}

\frac{d}{d x} (ln (16 - 4 x^{2} - 4 y^{2} - z^{2}))

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

x \to 0 - lim (\frac{1}{sin ( x )})

- 5 + 9 x

\frac{d y}{d t} = 2 t y^{2}

What is (\partial)/(\partial x)((4y)/(x^5)) ?
The answer to (\partial)/(\partial x)((4y)/(x^5)) is -(20y)/(x^6)