What is the derivative of ln((x^3/(e^{3x)})) ?

The derivative of ln((x^3/(e^{3x)})) is 3/x-3

What is the first derivative of ln((x^3/(e^{3x)})) ?

The first derivative of ln((x^3/(e^{3x)})) is 3/x-3

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{x ^{3}}{e ^{3 x}}))

\frac{3}{x} - 3

Solution steps

\frac{d}{d x} (ln (\frac{x ^{3}}{e ^{3 x}}))

Simplify

ln (\frac{x ^{3}}{e ^{3 x}}) : ln (x^{3}) - 3 x

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (ln (x^{3})) = \frac{3}{x}

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

= \frac{3}{x} - 3

What is the derivative of ln((x^3/(e^{3x)})) ?
The derivative of ln((x^3/(e^{3x)})) is 3/x-3
What is the first derivative of ln((x^3/(e^{3x)})) ?
The first derivative of ln((x^3/(e^{3x)})) is 3/x-3