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}

x^{(2)} - 2 x + 2

x^{(2)} - 2 x + 3

c e^{t} - d e^{t}

3 a x + 3 x + 4 y + 4 a y

(- 54 x^{4} yz) + (6 x^{5} y)