What is the derivative of (sqrt(x)-2)/(x-4) ?

The derivative of (sqrt(x)-2)/(x-4) is (-x+4sqrt(x)-4)/(2sqrt(x)(x-4)^2)

What is the first derivative of (sqrt(x)-2)/(x-4) ?

The first derivative of (sqrt(x)-2)/(x-4) is (-x+4sqrt(x)-4)/(2sqrt(x)(x-4)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{x - 2}{x - 4}

\frac{- x + 4 x - 4}{2 x ( x - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 2}{x - 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 2 ) ( x - 4 ) - \frac{d}{d x} ( x - 4 ) ( x - 2 )}{( x - 4 ) ^{2}}

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

\frac{d}{d x} (x - 4) = 1

= \frac{\frac{1}{2 x} ( x - 4 ) - 1 \cdot ( x - 2 )}{( x - 4 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x - 4 ) - 1 \cdot ( x - 2 )}{( x - 4 ) ^{2}} : \frac{- x + 4 x - 4}{2 x ( x - 4 ) ^{2}}

= \frac{- x + 4 x - 4}{2 x ( x - 4 ) ^{2}}

d er i v a t i v e f (x) = x (1 - x)^{4}

Δ x \to 0 lim (\frac{0}{Δ x ^{2}})

n \to \infty lim (x^{n})

y^{^{'}} + 2 y = 0, y (0) = 0

a re a y = 5 x^{2}, y = x^{2} + 2

What is the derivative of (sqrt(x)-2)/(x-4) ?
The derivative of (sqrt(x)-2)/(x-4) is (-x+4sqrt(x)-4)/(2sqrt(x)(x-4)^2)
What is the first derivative of (sqrt(x)-2)/(x-4) ?
The first derivative of (sqrt(x)-2)/(x-4) is (-x+4sqrt(x)-4)/(2sqrt(x)(x-4)^2)