What is (\partial)/(\partial y)(xy(x-2)(y+3)) ?

The answer to (\partial)/(\partial y)(xy(x-2)(y+3)) is x(x-2)(2y+3)

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(\partial)/(\partial y)(xy(x-2)(y+3))

\frac{\partial}{\partial y} (x y (x - 2) (y + 3))

x (x - 2) (2 y + 3)

Solution steps

\frac{\partial}{\partial y} (x y (x - 2) (y + 3))

Treat

x

as a constant

Take the constant out:

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

= x (x - 2) \frac{\partial}{\partial y} (y (y + 3))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = y + 3

= x (x - 2) (\frac{\partial}{\partial y} (y) (y + 3) + \frac{\partial}{\partial y} (y + 3) y)

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (y + 3) = 1

= x (x - 2) (1 \cdot (y + 3) + 1 \cdot y)

Simplify

x (x - 2) (1 \cdot (y + 3) + 1 \cdot y) : x (x - 2) (2 y + 3)

= x (x - 2) (2 y + 3)

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What is (\partial)/(\partial y)(xy(x-2)(y+3)) ?
The answer to (\partial)/(\partial y)(xy(x-2)(y+3)) is x(x-2)(2y+3)