What is the d/(dy)((x^2)/((x-y)^2)) ?

The d/(dy)((x^2)/((x-y)^2)) is (2x^2)/((x-y)^3)

What is the first d/(dy)((x^2)/((x-y)^2)) ?

The first d/(dy)((x^2)/((x-y)^2)) is (2x^2)/((x-y)^3)

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\frac{d}{d y} (\frac{x ^{2}}{( x - y ) ^{2}})

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

Solution steps

\frac{d}{d y} (\frac{x ^{2}}{( x - y ) ^{2}})

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d y} (x - y) = - 1

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

Simplify

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

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

What is the d/(dy)((x^2)/((x-y)^2)) ?
The d/(dy)((x^2)/((x-y)^2)) is (2x^2)/((x-y)^3)
What is the first d/(dy)((x^2)/((x-y)^2)) ?
The first d/(dy)((x^2)/((x-y)^2)) is (2x^2)/((x-y)^3)