en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=ln((x-1)/(x+3))-x

Solution

derivative of

y = ln (\frac{x - 1}{x + 3}) - x

Solution

\frac{4}{( x - 1 ) ( x + 3 )} - 1

Solution steps

\frac{d}{d x} (ln (\frac{x - 1}{x + 3}) - x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (ln (\frac{x - 1}{x + 3})) = \frac{4}{( x - 1 ) ( x + 3 )}

\frac{d x}{d x} = 1

= \frac{4}{( x - 1 ) ( x + 3 )} - 1

Graph

Popular Examples

limit as x approaches c of 13/3+2/3

x \to c lim (\frac{13}{3} + \frac{2}{3})

inverse oflaplace (s+1)/(s^2)inverse laplace

\frac{s + 1}{s ^{2}}

area 7x-x^2,2x,(5,10)area

7 x - x^{2}, 2 x, (5, 10)

integral of (5x+3)/(x^2+2x-3)

\int \frac{5 x + 3}{x ^{2} + 2 x - 3} d x

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

\frac{d}{d x} (2 x^{3} + 5 x)

Frequently Asked Questions (FAQ)

What is the derivative of y=ln((x-1)/(x+3))-x ?
The derivative of y=ln((x-1)/(x+3))-x is 4/((x-1)(x+3))-1
What is the first derivative of y=ln((x-1)/(x+3))-x ?
The first derivative of y=ln((x-1)/(x+3))-x is 4/((x-1)(x+3))-1