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

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

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

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

2 x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= x (0 + 2)

Simplify

= 2 x

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