What is the derivative of (sqrt(x)-5)/(x-25) ?

The derivative of (sqrt(x)-5)/(x-25) is (-x+10sqrt(x)-25)/(2sqrt(x)(x-25)^2)

What is the first derivative of (sqrt(x)-5)/(x-25) ?

The first derivative of (sqrt(x)-5)/(x-25) is (-x+10sqrt(x)-25)/(2sqrt(x)(x-25)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{x - 5}{x - 25}

\frac{- x + 10 x - 25}{2 x ( x - 25 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 5}{x - 25})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 5 ) ( x - 25 ) - \frac{d}{d x} ( x - 25 ) ( x - 5 )}{( x - 25 ) ^{2}}

\frac{d}{d x} (x - 5) = \frac{1}{2 x}

\frac{d}{d x} (x - 25) = 1

= \frac{\frac{1}{2 x} ( x - 25 ) - 1 \cdot ( x - 5 )}{( x - 25 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x - 25 ) - 1 \cdot ( x - 5 )}{( x - 25 ) ^{2}} : \frac{- x + 10 x - 25}{2 x ( x - 25 ) ^{2}}

= \frac{- x + 10 x - 25}{2 x ( x - 25 ) ^{2}}

\int_{0}^{1} (x^{2} + 1) e^{- 1} d x

\int \frac{5}{1000 + t} d t

\int x^{2} (4 - x) d x

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

\frac{d}{d x} (20 x - x^{2})

What is the derivative of (sqrt(x)-5)/(x-25) ?
The derivative of (sqrt(x)-5)/(x-25) is (-x+10sqrt(x)-25)/(2sqrt(x)(x-25)^2)
What is the first derivative of (sqrt(x)-5)/(x-25) ?
The first derivative of (sqrt(x)-5)/(x-25) is (-x+10sqrt(x)-25)/(2sqrt(x)(x-25)^2)