What is the derivative of (x-1sqrt(x^2-2x+2)) ?

The derivative of (x-1sqrt(x^2-2x+2)) is (2x^2-4x+3)/(sqrt(x^2-2x+2))

What is the first derivative of (x-1sqrt(x^2-2x+2)) ?

The first derivative of (x-1sqrt(x^2-2x+2)) is (2x^2-4x+3)/(sqrt(x^2-2x+2))

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^{2} - 2 x + 2)

\frac{2 x ^{2} - 4 x + 3}{x ^{2} - 2 x + 2}

Solution steps

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

Apply the Product Rule:

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

f = x - 1, g = x^{2} - 2 x + 2

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

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

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

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

Simplify

1 \cdot x^{2} - 2 x + 2 + \frac{x - 1}{x ^{2} - 2 x + 2} (x - 1) : \frac{2 x ^{2} - 4 x + 3}{x ^{2} - 2 x + 2}

= \frac{2 x ^{2} - 4 x + 3}{x ^{2} - 2 x + 2}

What is the derivative of (x-1sqrt(x^2-2x+2)) ?
The derivative of (x-1sqrt(x^2-2x+2)) is (2x^2-4x+3)/(sqrt(x^2-2x+2))
What is the first derivative of (x-1sqrt(x^2-2x+2)) ?
The first derivative of (x-1sqrt(x^2-2x+2)) is (2x^2-4x+3)/(sqrt(x^2-2x+2))