What is (\partial)/(\partial x)(xy(1-xy)) ?

The answer to (\partial)/(\partial x)(xy(1-xy)) is y(1-2xy)

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(\partial)/(\partial x)(xy(1-xy))

\frac{\partial}{\partial x} (x y (1 - x y))

y (1 - 2 x y)

Solution steps

\frac{\partial}{\partial x} (x y (1 - x y))

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = 1 - x y

= y (\frac{\partial}{\partial x} (x) (1 - x y) + \frac{\partial}{\partial x} (1 - x y) x)

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

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

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

Simplify

= y (1 - 2 x y)

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What is (\partial)/(\partial x)(xy(1-xy)) ?
The answer to (\partial)/(\partial x)(xy(1-xy)) is y(1-2xy)