What is (\partial)/(\partial x)(-3x(-9-x-2y)) ?

The answer to (\partial)/(\partial x)(-3x(-9-x-2y)) is -3(-2x-2y-9)

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(\partial)/(\partial x)(-3x(-9-x-2y))

\frac{\partial}{\partial x} (- 3 x (- 9 - x - 2 y))

- 3 (- 2 x - 2 y - 9)

Solution steps

\frac{\partial}{\partial x} (- 3 x (- 9 - x - 2 y))

Treat

y

as a constant

Take the constant out:

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

= - 3 \frac{\partial}{\partial x} (x (- 9 - x - 2 y))

Apply the Product Rule:

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

f = x, g = - 9 - x - 2 y

= - 3 (\frac{\partial}{\partial x} (x) (- 9 - x - 2 y) + \frac{\partial}{\partial x} (- 9 - x - 2 y) x)

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

\frac{\partial}{\partial x} (- 9 - x - 2 y) = - 1

= - 3 (1 \cdot (- 9 - x - 2 y) + (- 1) x)

Simplify

- 3 (1 \cdot (- 9 - x - 2 y) + (- 1) x) : - 3 (- 2 x - 2 y - 9)

= - 3 (- 2 x - 2 y - 9)

\frac{d y}{d t} t = y + 6 t^{2} sin (t)

0.2 t

\int x x^{2} - 4 d x

\frac{d y}{d x} - 7 y = x e^{2 x}

\frac{d}{d x} (\frac{4 x + 3}{5 e ^{x}})

What is (\partial)/(\partial x)(-3x(-9-x-2y)) ?
The answer to (\partial)/(\partial x)(-3x(-9-x-2y)) is -3(-2x-2y-9)