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

The d/(dy)((x(y))(y^2)) is 3xy^2

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

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

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

3 x y^{2}

Solution steps

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

Simplify

(x (y)) (y^{2}) : x y^{3}

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 3 x y^{2}

[- 4.4]

(1 + cos (2 θ)) (1 - cos (2 θ))

f (t)^{2}

cos (270 - 2 x)

d (ln (x))