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

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

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

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

- 4 x - y + 3

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = 3 - 2 x - y

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

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

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

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

Simplify

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

= - 4 x - y + 3

\int e^{x} + 5 d x

\frac{\partial}{\partial x} (8 x y^{2})

\int π (e^{- x})^{2} d x

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