What is expand (x-y) d/(dy)(xy+2) ?

The solution to expand (x-y) d/(dy)(xy+2) is x d/(dy)(xy+2)-y d/(dy)(xy+2)

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expand (x-y) d/(dy)(xy+2)

expand

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

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

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{d}{d y} (x y + 2), b = x, c = y

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

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

\frac{2 ( 2 + 10 )}{3}

(\frac{x}{2} - \frac{3}{4}) (\frac{x}{2} + \frac{3}{4})

\frac{( 2 x - 1 ) ( x + 3 )}{x + 1}

\frac{1}{( x ^{2} + 5 ) ^{6}}

\frac{( n + 1 ) ^{2} \cdot ( n + 2 ) ^{2}}{4}

What is expand (x-y) d/(dy)(xy+2) ?
The solution to expand (x-y) d/(dy)(xy+2) is x d/(dy)(xy+2)-y d/(dy)(xy+2)