What is the derivative of ln(3x^2+7) ?

The derivative of ln(3x^2+7) is (6x)/(3x^2+7)

What is the first derivative of ln(3x^2+7) ?

The first derivative of ln(3x^2+7) is (6x)/(3x^2+7)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (ln (3 x^{2} + 7))

\frac{6 x}{3 x ^{2} + 7}

Solution steps

\frac{d}{d x} (ln (3 x^{2} + 7))

Apply the chain rule:

\frac{1}{3 x ^{2} + 7} \frac{d}{d x} (3 x^{2} + 7)

= \frac{1}{3 x ^{2} + 7} \frac{d}{d x} (3 x^{2} + 7)

\frac{d}{d x} (3 x^{2} + 7) = 6 x

= \frac{1}{3 x ^{2} + 7} \cdot 6 x

Simplify

\frac{1}{3 x ^{2} + 7} \cdot 6 x : \frac{6 x}{3 x ^{2} + 7}

= \frac{6 x}{3 x ^{2} + 7}

What is the derivative of ln(3x^2+7) ?
The derivative of ln(3x^2+7) is (6x)/(3x^2+7)
What is the first derivative of ln(3x^2+7) ?
The first derivative of ln(3x^2+7) is (6x)/(3x^2+7)