What is (\partial)/(\partial x)((4y)/(x^3)) ?

The answer to (\partial)/(\partial x)((4y)/(x^3)) is -(12y)/(x^4)

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(\partial)/(\partial x)((4y)/(x^3))

\frac{\partial}{\partial x} (\frac{4 y}{x ^{3}})

- \frac{12 y}{x ^{4}}

Solution steps

\frac{\partial}{\partial x} (\frac{4 y}{x ^{3}})

Treat

y

as a constant

Take the constant out:

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

= 4 y \frac{\partial}{\partial x} (\frac{1}{x ^{3}})

Apply exponent rule:

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

= 4 y \frac{\partial}{\partial x} (x^{- 3})

Apply the Power Rule:

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

= 4 y (- 3 x^{- 3 - 1})

Simplify

4 y (- 3 x^{- 3 - 1}) : - \frac{12 y}{x ^{4}}

= - \frac{12 y}{x ^{4}}

n = 0 \sum \infty \infty

\frac{s + 1}{s ^{2} + 2 s + 10}

\int \frac{2 \cdot x ^{2} - x + 2}{x ^{5} + 2 \cdot x ^{3} + x} d x

\int - x^{2} - 4 x d x

\int (tan (x))^{3} sec (x) d x

What is (\partial)/(\partial x)((4y)/(x^3)) ?
The answer to (\partial)/(\partial x)((4y)/(x^3)) is -(12y)/(x^4)