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

The derivative of ln(x^3+3) is (3x^2)/(x^3+3)

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

The first derivative of ln(x^3+3) is (3x^2)/(x^3+3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{3 x ^{2}}{x ^{3} + 3}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{x ^{3} + 3} \cdot 3 x^{2}

Simplify

\frac{1}{x ^{3} + 3} \cdot 3 x^{2} : \frac{3 x ^{2}}{x ^{3} + 3}

= \frac{3 x ^{2}}{x ^{3} + 3}

x \to 0 lim (\frac{x}{x - 1})

x \to 0 lim (x - 4)

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

\int \frac{1}{( 1 + x ^{2} ) ^{\frac{3}{2}}} d x

\int \frac{5}{( x + 2 ) ^{2}} d x

What is the derivative of ln(x^3+3) ?
The derivative of ln(x^3+3) is (3x^2)/(x^3+3)
What is the first derivative of ln(x^3+3) ?
The first derivative of ln(x^3+3) is (3x^2)/(x^3+3)