What is the d/(dy)(1/(x-y)) ?

The d/(dy)(1/(x-y)) is 1/((x-y)^2)

What is the first d/(dy)(1/(x-y)) ?

The first d/(dy)(1/(x-y)) is 1/((x-y)^2)

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

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

Solution steps

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

Treat

x

as a constant

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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