What is the derivative of ln((4x^2/(x-6))) ?

The derivative of ln((4x^2/(x-6))) is (x-12)/(x(x-6))

What is the first derivative of ln((4x^2/(x-6))) ?

The first derivative of ln((4x^2/(x-6))) is (x-12)/(x(x-6))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (ln (\frac{4 x ^{2}}{x - 6}))

\frac{x - 12}{x ( x - 6 )}

Solution steps

\frac{d}{d x} (ln (\frac{4 x ^{2}}{x - 6}))

Apply the chain rule:

\frac{1}{\frac{4 x ^{2}}{x - 6}} \frac{d}{d x} (\frac{4 x ^{2}}{x - 6})

= \frac{1}{\frac{4 x ^{2}}{x - 6}} \frac{d}{d x} (\frac{4 x ^{2}}{x - 6})

\frac{d}{d x} (\frac{4 x ^{2}}{x - 6}) = \frac{4 ( x ^{2} - 12 x )}{( x - 6 ) ^{2}}

= \frac{1}{\frac{4 x ^{2}}{x - 6}} \cdot \frac{4 ( x ^{2} - 12 x )}{( x - 6 ) ^{2}}

Simplify

\frac{1}{\frac{4 x ^{2}}{x - 6}} \cdot \frac{4 ( x ^{2} - 12 x )}{( x - 6 ) ^{2}} : \frac{x - 12}{x ( x - 6 )}

= \frac{x - 12}{x ( x - 6 )}

What is the derivative of ln((4x^2/(x-6))) ?
The derivative of ln((4x^2/(x-6))) is (x-12)/(x(x-6))
What is the first derivative of ln((4x^2/(x-6))) ?
The first derivative of ln((4x^2/(x-6))) is (x-12)/(x(x-6))