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

The d/(dy)(x^2+2xy+y^2) is 2x+2y

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

The first d/(dy)(x^2+2xy+y^2) is 2x+2y

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

2 x + 2 y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d y} (x^{2}) = 0

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

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

= 0 + 2 x + 2 y

Simplify

= 2 x + 2 y

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