What is (\partial)/(\partial x)(-4xy(3-x-y)) ?

The answer to (\partial)/(\partial x)(-4xy(3-x-y)) is -4y(-2x-y+3)

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(\partial)/(\partial x)(-4xy(3-x-y))

\frac{\partial}{\partial x} (- 4 x y (3 - x - y))

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

Solution steps

\frac{\partial}{\partial x} (- 4 x y (3 - x - y))

Treat

y

as a constant

Take the constant out:

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

= - 4 y \frac{\partial}{\partial x} (x (3 - x - y))

Apply the Product Rule:

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

f = x, g = 3 - x - y

= - 4 y (\frac{\partial}{\partial x} (x) (3 - x - y) + \frac{\partial}{\partial x} (3 - x - y) x)

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

\frac{\partial}{\partial x} (3 - x - y) = - 1

= - 4 y (1 \cdot (3 - x - y) + (- 1) x)

Simplify

- 4 y (1 \cdot (3 - x - y) + (- 1) x) : - 4 y (- 2 x - y + 3)

= - 4 y (- 2 x - y + 3)

y^{^{''}} + 2 y^{^{'}} + 37 y = 5 e^{- t} cos (6 t)

\int e^{a x} sin (0 x) d x

f (x) = 8 x - 3

x = 9 y^{2}, x = 4 + 5 y^{2}

f (x) = \frac{3 x + 4}{2 x + 1}

What is (\partial)/(\partial x)(-4xy(3-x-y)) ?
The answer to (\partial)/(\partial x)(-4xy(3-x-y)) is -4y(-2x-y+3)