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

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

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

The first derivative of (a+bx/(a-bx)) is (2ab)/((a-bx)^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 + b x}{a - b x})

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y^{^{'}} + 10 y = t + e^{- 5 t}

\frac{d}{d x} (x^{2} \cdot cos (x^{2}))

\int (e^{- x} + 4^{x}) d x

G (r) = r + 4 r

\int \frac{1}{x ^{2} - 8 x} d x

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