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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int 3 e^{- x} d x

n = 1 \sum \infty n^{2} \cdot e^{- n^{3}}

\int \frac{3 x ^{2}}{( x ^{3} + 1 ) ^{2}} d x

x \to 0 + lim (x^{4} ln (x))

2 cos (2 y)

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