What is the derivative of ln(x^4+2) ?

The derivative of ln(x^4+2) is (4x^3)/(x^4+2)

What is the first derivative of ln(x^4+2) ?

The first derivative of ln(x^4+2) is (4x^3)/(x^4+2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

ln (x^{4} + 2)

\frac{4 x ^{3}}{x ^{4} + 2}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{4 x ^{3}}{x ^{4} + 2}

What is the derivative of ln(x^4+2) ?
The derivative of ln(x^4+2) is (4x^3)/(x^4+2)
What is the first derivative of ln(x^4+2) ?
The first derivative of ln(x^4+2) is (4x^3)/(x^4+2)