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

The d/(dy)((x(y))(y^3)) is 4xy^3

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

The first d/(dy)((x(y))(y^3)) is 4xy^3

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

4 x y^{3}

Solution steps

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

Simplify

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

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 4 x y^{3}

x^{2 n - 4} - y^{4 n - 12}

(a + b) + (b^{'} c)

\frac{2}{x ^{2} + 10 x + 24}

f (x) = 2 x + 7

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