What is the derivative of xsqrt(1-x) ?

The derivative of xsqrt(1-x) is (-3x+2)/(2sqrt(1-x))

What is the first derivative of xsqrt(1-x) ?

The first derivative of xsqrt(1-x) is (-3x+2)/(2sqrt(1-x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (x 1 - x)

\frac{- 3 x + 2}{2 1 - x}

Solution steps

\frac{d}{d x} (x 1 - x)

Apply the Product Rule:

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

f = x, g = 1 - x

= \frac{d x}{d x} 1 - x + \frac{d}{d x} (1 - x) x

\frac{d x}{d x} = 1

\frac{d}{d x} (1 - x) = - \frac{1}{2 1 - x}

= 1 \cdot 1 - x + (- \frac{1}{2 1 - x}) x

Simplify

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

= \frac{- 3 x + 2}{2 1 - x}

What is the derivative of xsqrt(1-x) ?
The derivative of xsqrt(1-x) is (-3x+2)/(2sqrt(1-x))
What is the first derivative of xsqrt(1-x) ?
The first derivative of xsqrt(1-x) is (-3x+2)/(2sqrt(1-x))