What is (\partial)/(\partial x)(x/(x^2-x+1)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(x/(x^2-x+1))

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

h \to 0 lim (tan (h))

\frac{d}{d t} (t e^{2 t})

\int (x + 1) e^{5 x^{2} + 10 x} d x

(1 + 9 x^{2}) (x - x^{2})

\frac{d}{d x} (7 x (sin (x) + cos (x)))

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