What is the derivative of ln(4x^3) ?

The derivative of ln(4x^3) is 3/x

What is the first derivative of ln(4x^3) ?

The first derivative of ln(4x^3) is 3/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

ln (4 x^{3})

\frac{3}{x}

Solution steps

\frac{d}{d x} (ln (4 x^{3}))

Apply the chain rule:

\frac{1}{4 x ^{3}} \frac{d}{d x} (4 x^{3})

= \frac{1}{4 x ^{3}} \frac{d}{d x} (4 x^{3})

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

= \frac{1}{4 x ^{3}} \cdot 12 x^{2}

Simplify

\frac{1}{4 x ^{3}} \cdot 12 x^{2} : \frac{3}{x}

= \frac{3}{x}

\int \frac{x ^{5} - 1}{x} d x

\int \frac{1}{x ^{2} - 4 x + 8} d x

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

\int \frac{2 x - 3}{2 x + 1} d x

\int - 4 sin (5 x) sin (x) d x

What is the derivative of ln(4x^3) ?
The derivative of ln(4x^3) is 3/x
What is the first derivative of ln(4x^3) ?
The first derivative of ln(4x^3) is 3/x