en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=(x^2)/(x-11)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x - 11) = 1

= \frac{2 x ( x - 11 ) - 1 \cdot x ^{2}}{( x - 11 ) ^{2}}

Simplify

\frac{2 x ( x - 11 ) - 1 \cdot x ^{2}}{( x - 11 ) ^{2}} : \frac{x ^{2} - 22 x}{( x - 11 ) ^{2}}

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

Popular Examples

limit as x approaches infinity of (e^{5x})/(9x^4+31x+1)

x \to \infty lim (\frac{e ^{5 x}}{9 x ^{4} + 31 x + 1})

derivative of sec^2(2x+4*2)

\frac{d}{d x} (sec^{2} (2 x + 4) \cdot 2)

derivative of f(x)=(f(x))/(x^7)derivative of

f (x) = \frac{f ( x )}{x ^{7}}

derivative of sqrt(5x^3+2x^2+3)derivative of

5 x^{3} + 2 x^{2} + 3

limit as x approaches infinity of cox(x)

x \to \infty lim (co x (x))

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^2)/(x-11) ?
The derivative of f(x)=(x^2)/(x-11) is (x^2-22x)/((x-11)^2)
What is the first derivative of f(x)=(x^2)/(x-11) ?
The first derivative of f(x)=(x^2)/(x-11) is (x^2-22x)/((x-11)^2)