What is the first d/(dy)((x)(8x^3)) ?

The first d/(dy)((x)(8x^3)) is 32y^3

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d/(dy)((x)(8x^3))

\frac{d}{d y} ((y) (8 y^{3}))

32 y^{3}

Solution steps

\frac{d}{d y} ((y) (8 y^{3}))

Simplify

(y) (8 y^{3}) : 8 y^{4}

= \frac{d}{d y} (8 y^{4})

Take the constant out:

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

= 8 \frac{d}{d y} (y^{4})

Apply the Power Rule:

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

= 8 \cdot 4 y^{4 - 1}

Simplify

= 32 y^{3}

\frac{1}{2} x^{2} - 31

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