What is the first d/(dy)(4y^3) ?

The first d/(dy)(4y^3) is 12y^2

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d/(dy)(4y^3)

\frac{d}{d y} (4 y^{3})

12 y^{2}

Solution steps

\frac{d}{d y} (4 y^{3})

Take the constant out:

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

= 4 \frac{d}{d y} (y^{3})

Apply the Power Rule:

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

= 4 \cdot 3 y^{3 - 1}

Simplify

= 12 y^{2}

\int_{0}^{9} (2 x^{3} + 1) d x

\frac{d}{d x} (3 x^{2} - 1)

\int (x^{2} + 1)^{- 1} d x

f (x) = 4^{x} - x^{2} + 3 ln (x)