What is (\partial)/(\partial x)(xy(18-x-y)) ?

The answer to (\partial)/(\partial x)(xy(18-x-y)) is y(-2x-y+18)

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(\partial)/(\partial x)(xy(18-x-y))

\frac{\partial}{\partial x} (x y (18 - x - y))

y (- 2 x - y + 18)

Solution steps

\frac{\partial}{\partial x} (x y (18 - x - y))

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (x (18 - x - y))

Apply the Product Rule:

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

f = x, g = 18 - x - y

= y (\frac{\partial}{\partial x} (x) (18 - x - y) + \frac{\partial}{\partial x} (18 - x - y) x)

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

\frac{\partial}{\partial x} (18 - x - y) = - 1

= y (1 \cdot (18 - x - y) + (- 1) x)

Simplify

y (1 \cdot (18 - x - y) + (- 1) x) : y (- 2 x - y + 18)

= y (- 2 x - y + 18)

\int e^{c o s (x)} (- sin (x)) d x

\int (x^{2} - 3)^{5} x d x

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

(x^{2} + 2 y^{2}) = x y y^{^{'}}

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

What is (\partial)/(\partial x)(xy(18-x-y)) ?
The answer to (\partial)/(\partial x)(xy(18-x-y)) is y(-2x-y+18)