What is the first d/(dy)(2xy^3) ?

The first d/(dy)(2xy^3) is 6xy^2

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d/(dy)(2xy^3)

\frac{d}{d y} (2 x y^{3})

6 x y^{2}

Solution steps

\frac{d}{d y} (2 x y^{3})

Treat

x

as a constant

Take the constant out:

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

= 2 x \frac{d}{d y} (y^{3})

Apply the Power Rule:

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

= 2 x \cdot 3 y^{3 - 1}

Simplify

= 6 x y^{2}

\int - \frac{1}{s} e^{- s t} d t

\int x (4 x + 5)^{8} d x

x \to \infty lim (5^{- \frac{1}{x}})

f (x) = x^{7} - x^{3}

y = sin (\frac{1}{x})