What is (\partial)/(\partial x)(xy(1-x-y)) ?

The answer to (\partial)/(\partial x)(xy(1-x-y)) is y(-2x-y+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(xy(1-x-y))

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

y (- 2 x - y + 1)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = 1 - x - y

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

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

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

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

Simplify

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

= y (- 2 x - y + 1)

\frac{d}{d x} (\frac{2}{sin ( x )})

sin (2 x), 0

\frac{d}{d x} (e^{- \frac{x}{6}})

y = x^{2} - 5

\frac{d}{d t} (\frac{e ^{- t}}{1 + t ^{2}})

What is (\partial)/(\partial x)(xy(1-x-y)) ?
The answer to (\partial)/(\partial x)(xy(1-x-y)) is y(-2x-y+1)