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

The answer to (\partial)/(\partial x)((3y)/(x^5)) is -(15y)/(x^6)

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

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

- \frac{15 y}{x ^{6}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

3 y (- 5 x^{- 5 - 1}) : - \frac{15 y}{x ^{6}}

= - \frac{15 y}{x ^{6}}

\int_{2}^{\infty} e^{- \frac{x}{3}} d x

cos (sin (x^{3}))

y^{3} - (18 x + 4) + 3 x y^{2} y^{^{'}} = 0

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

\frac{d}{d x} (arcsech (1 - x^{2}))

What is (\partial)/(\partial x)((3y)/(x^5)) ?
The answer to (\partial)/(\partial x)((3y)/(x^5)) is -(15y)/(x^6)