What is (\partial)/(\partial x)(-xy(-15-x-y)) ?

The answer to (\partial)/(\partial x)(-xy(-15-x-y)) is -y(-2x-y-15)

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(\partial)/(\partial x)(-xy(-15-x-y))

\frac{\partial}{\partial x} (- x y (- 15 - x - y))

- y (- 2 x - y - 15)

Solution steps

\frac{\partial}{\partial x} (- x y (- 15 - x - y))

Treat

y

as a constant

Take the constant out:

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

= - y \frac{\partial}{\partial x} (x (- 15 - x - y))

Apply the Product Rule:

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

f = x, g = - 15 - x - y

= - y (\frac{\partial}{\partial x} (x) (- 15 - x - y) + \frac{\partial}{\partial x} (- 15 - x - y) x)

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

\frac{\partial}{\partial x} (- 15 - x - y) = - 1

= - y (1 \cdot (- 15 - x - y) + (- 1) x)

Simplify

- y (1 \cdot (- 15 - x - y) + (- 1) x) : - y (- 2 x - y - 15)

= - y (- 2 x - y - 15)

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

\frac{d y}{d t} = \frac{t}{y - 2}, y (- 1) = 0

\frac{d}{d x} (\frac{3}{5 x ^{2}})

\int sin (x) sin (2 x) cos (3 x) d x

What is (\partial)/(\partial x)(-xy(-15-x-y)) ?
The answer to (\partial)/(\partial x)(-xy(-15-x-y)) is -y(-2x-y-15)