What is the derivative of ln(sqrt((4x-4)/(5x+9))) ?

The derivative of ln(sqrt((4x-4)/(5x+9))) is 7/((x-1)(5x+9))

What is the first derivative of ln(sqrt((4x-4)/(5x+9))) ?

The first derivative of ln(sqrt((4x-4)/(5x+9))) is 7/((x-1)(5x+9))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

ln (\frac{4 x - 4}{5 x + 9})

\frac{7}{( x - 1 ) ( 5 x + 9 )}

Solution steps

\frac{d}{d x} (ln (\frac{4 x - 4}{5 x + 9}))

Apply the chain rule:

\frac{1}{\frac{4 x - 4}{5 x + 9}} \frac{d}{d x} (\frac{4 x - 4}{5 x + 9})

= \frac{1}{\frac{4 x - 4}{5 x + 9}} \frac{d}{d x} (\frac{4 x - 4}{5 x + 9})

\frac{d}{d x} (\frac{4 x - 4}{5 x + 9}) = \frac{14}{x - 1 ( 5 x + 9 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{4 x - 4}{5 x + 9}} \cdot \frac{14}{x - 1 ( 5 x + 9 ) ^{\frac{3}{2}}}

Simplify

\frac{1}{\frac{4 x - 4}{5 x + 9}} \cdot \frac{14}{x - 1 ( 5 x + 9 ) ^{\frac{3}{2}}} : \frac{7}{( x - 1 ) ( 5 x + 9 )}

= \frac{7}{( x - 1 ) ( 5 x + 9 )}

x y^{^{'}} - 3 y = 6

\frac{\partial}{\partial x} (e^{x^{2} + 2 y})

y = 10 x, y = x^{2}

3 x^{2} + 24 x - y^{2} + 2 y = - 44

\frac{d}{d x} (1 + tan (x))

What is the derivative of ln(sqrt((4x-4)/(5x+9))) ?
The derivative of ln(sqrt((4x-4)/(5x+9))) is 7/((x-1)(5x+9))
What is the first derivative of ln(sqrt((4x-4)/(5x+9))) ?
The first derivative of ln(sqrt((4x-4)/(5x+9))) is 7/((x-1)(5x+9))