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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 lim (\frac{2 x + 1}{∣ x ∣})

y^{^{''}} - 4 y^{^{'}} - 4 y = 0

\int_{0}^{π} x^{2} sin^{2} (x) d x

\frac{sin ( x ^{2} - 5 )}{2 x}

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

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