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

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

Popular >

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

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

y (- 2 x - y + 3)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = 3 - x - y

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

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

\frac{\partial}{\partial x} (3 - x - y) = - 1

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

Simplify

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

= y (- 2 x - y + 3)

x \to π lim (sin (\frac{7}{6} x))

\int \frac{1}{e ^{x + 1}} d x

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

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

\int_{2 y}^{2} \int_{0}^{1} e^{x^{2}} d y d x

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