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

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

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d/(dy)((x)(xy^2))

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

2 x^{2} y

Solution steps

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

Simplify

(x) (x y^{2}) : x^{2} y^{2}

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= x^{2} \cdot 2 y^{2 - 1}

Simplify

= 2 x^{2} y

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4 x^{3 + 3 x^{2} + 5 x + 9}

[ab]

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