What is the derivative of (x^2-11x+10/(x^2+11x+10)) ?

The derivative of (x^2-11x+10/(x^2+11x+10)) is (22x^2-220)/((x^2+11x+10)^2)

What is the first derivative of (x^2-11x+10/(x^2+11x+10)) ?

The first derivative of (x^2-11x+10/(x^2+11x+10)) is (22x^2-220)/((x^2+11x+10)^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{x ^{2} - 11 x + 10}{x ^{2} + 11 x + 10})

\frac{22 x ^{2} - 220}{( x ^{2} + 11 x + 10 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 11 x + 10}{x ^{2} + 11 x + 10})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 11 x + 10 ) ( x ^{2} + 11 x + 10 ) - \frac{d}{d x} ( x ^{2} + 11 x + 10 ) ( x ^{2} - 11 x + 10 )}{( x ^{2} + 11 x + 10 ) ^{2}}

\frac{d}{d x} (x^{2} - 11 x + 10) = 2 x - 11

\frac{d}{d x} (x^{2} + 11 x + 10) = 2 x + 11

= \frac{( 2 x - 11 ) ( x ^{2} + 11 x + 10 ) - ( 2 x + 11 ) ( x ^{2} - 11 x + 10 )}{( x ^{2} + 11 x + 10 ) ^{2}}

Expand

(2 x - 11) (x^{2} + 11 x + 10) - (2 x + 11) (x^{2} - 11 x + 10) : 22 x^{2} - 220

= \frac{22 x ^{2} - 220}{( x ^{2} + 11 x + 10 ) ^{2}}

\frac{d}{d x} (\frac{x ^{2} - 2}{5 x ^{3} + 6})

\frac{\partial}{\partial x} (a^{2} - x^{2})

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

f (x) = ln (ln (3 x))

\frac{d}{d x} (\frac{x ^{2}}{x + 7})

What is the derivative of (x^2-11x+10/(x^2+11x+10)) ?
The derivative of (x^2-11x+10/(x^2+11x+10)) is (22x^2-220)/((x^2+11x+10)^2)
What is the first derivative of (x^2-11x+10/(x^2+11x+10)) ?
The first derivative of (x^2-11x+10/(x^2+11x+10)) is (22x^2-220)/((x^2+11x+10)^2)