What is the derivative of (a-x/(a+x)) ?

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

What is the first derivative of (a-x/(a+x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (a + x) = 1

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

Simplify

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

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

f (x) = ln (1 + e^{x}), at x = ln (2)

\int x (x - 3)^{2} d x

g (t) = 2 t^{\frac{- 3}{4}}

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

6 ln (9 - x)

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