What is the d/(dy)((x)(xy^{-5})) ?

The d/(dy)((x)(xy^{-5})) is -(5x^2)/(y^6)

What is the first d/(dy)((x)(xy^{-5})) ?

The first d/(dy)((x)(xy^{-5})) is -(5x^2)/(y^6)

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\frac{d}{d y} ((x) (x y^{- 5}))

- \frac{5 x ^{2}}{y ^{6}}

Solution steps

\frac{d}{d y} ((x) (x y^{- 5}))

Treat

x

as a constant

Take the constant out:

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

= xx \frac{d}{d y} (y^{- 5})

Apply the Power Rule:

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

= xx (- 5 y^{- 5 - 1})

Simplify

xx (- 5 y^{- 5 - 1}) : - \frac{5 x ^{2}}{y ^{6}}

= - \frac{5 x ^{2}}{y ^{6}}

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What is the d/(dy)((x)(xy^{-5})) ?
The d/(dy)((x)(xy^{-5})) is -(5x^2)/(y^6)
What is the first d/(dy)((x)(xy^{-5})) ?
The first d/(dy)((x)(xy^{-5})) is -(5x^2)/(y^6)