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

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

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d/(dy)((x)(x+y^2))

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

2 x y

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d x}{d y} = 0

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

= x (0 + 2 y)

Simplify

= 2 x y

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