What is the derivative of f(x)=(2-1/x)/(x-3) ?

The derivative of f(x)=(2-1/x)/(x-3) is (-2x^2+2x-3)/(x^2(x-3)^2)

What is the first derivative of f(x)=(2-1/x)/(x-3) ?

The first derivative of f(x)=(2-1/x)/(x-3) is (-2x^2+2x-3)/(x^2(x-3)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = \frac{2 - \frac{1}{x}}{x - 3}

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

Solution steps

\frac{d}{d x} (\frac{2 - \frac{1}{x}}{x - 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 - \frac{1}{x} ) ( x - 3 ) - \frac{d}{d x} ( x - 3 ) ( 2 - \frac{1}{x} )}{( x - 3 ) ^{2}}

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

\frac{d}{d x} (x - 3) = 1

= \frac{\frac{1}{x ^{2}} ( x - 3 ) - 1 \cdot ( 2 - \frac{1}{x} )}{( x - 3 ) ^{2}}

Simplify

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

= \frac{- 2 x ^{2} + 2 x - 3}{x ^{2} ( x - 3 ) ^{2}}

x \to - 2 - lim (g (x))

x \to 0 lim ((1 + \frac{x}{3})^{\frac{1}{x}})

\int (θ^{4} + sec^{2} (θ)) d θ

y = sin (2) (x), y = sin (3) (x), 0 \leq x \leq π

x - \frac{1}{x}

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