en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (ax+b/(cx-a))

Solution

\frac{d}{d x} (\frac{a x + b}{c x - a})

Solution

\frac{- a ^{2} - b c}{( c x - a ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{a x + b}{c x - a})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( a x + b ) ( c x - a ) - \frac{d}{d x} ( c x - a ) ( a x + b )}{( c x - a ) ^{2}}

\frac{d}{d x} (a x + b) = a

\frac{d}{d x} (c x - a) = c

= \frac{a ( c x - a ) - c ( a x + b )}{( c x - a ) ^{2}}

Expand

a (c x - a) - c (a x + b) : - a^{2} - b c

= \frac{- a ^{2} - b c}{( c x - a ) ^{2}}

Popular Examples

area x^2-3,y=1 area

x^{2} - 3, y = 1

derivative of (ln(x)^{cos(4x)})

\frac{d}{d x} ((ln (x))^{c o s (4 x)})

derivative of (x^2)/(12)derivative of

\frac{x ^{2}}{12}

limit as x approaches+3-of sin(pi+x)+1

x \to + 3 - lim (sin (π + x) + 1)

area y=20-x^2\land y=2x+5,-2<= x<= 8 area

y = 20 - x^{2} and y = 2 x + 5, - 2 \leq x \leq 8

Frequently Asked Questions (FAQ)

What is the derivative of (ax+b/(cx-a)) ?
The derivative of (ax+b/(cx-a)) is (-a^2-bc)/((cx-a)^2)
What is the first derivative of (ax+b/(cx-a)) ?
The first derivative of (ax+b/(cx-a)) is (-a^2-bc)/((cx-a)^2)