What is the derivative of ln(sqrt(((x-3))/(x-1))) ?

The derivative of ln(sqrt(((x-3))/(x-1))) is 1/((x-1)(x-3))

What is the first derivative of ln(sqrt(((x-3))/(x-1))) ?

The first derivative of ln(sqrt(((x-3))/(x-1))) is 1/((x-1)(x-3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x - 3}{x - 1}) = \frac{1}{x - 3 ( x - 1 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{x - 3}{x - 1}} \cdot \frac{1}{x - 3 ( x - 1 ) ^{\frac{3}{2}}}

Simplify

\frac{1}{\frac{x - 3}{x - 1}} \cdot \frac{1}{x - 3 ( x - 1 ) ^{\frac{3}{2}}} : \frac{1}{( x - 1 ) ( x - 3 )}

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

\int_{1}^{4} \frac{4}{x} d x

\int t^{3} cos (t^{2}) d t

x \to 5 + lim (\frac{5 - x}{∣ 5 - x ∣})

ln (4 x + 7)

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

What is the derivative of ln(sqrt(((x-3))/(x-1))) ?
The derivative of ln(sqrt(((x-3))/(x-1))) is 1/((x-1)(x-3))
What is the first derivative of ln(sqrt(((x-3))/(x-1))) ?
The first derivative of ln(sqrt(((x-3))/(x-1))) is 1/((x-1)(x-3))