What is the derivative of ln(sqrt(x^2+19)) ?

The derivative of ln(sqrt(x^2+19)) is x/(x^2+19)

What is the first derivative of ln(sqrt(x^2+19)) ?

The first derivative of ln(sqrt(x^2+19)) is x/(x^2+19)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (ln (x^{2} + 19))

\frac{x}{x ^{2} + 19}

Solution steps

\frac{d}{d x} (ln (x^{2} + 19))

Apply the chain rule:

\frac{1}{x ^{2} + 19} \frac{d}{d x} (x^{2} + 19)

= \frac{1}{x ^{2} + 19} \frac{d}{d x} (x^{2} + 19)

\frac{d}{d x} (x^{2} + 19) = \frac{x}{x ^{2} + 19}

= \frac{1}{x ^{2} + 19} \cdot \frac{x}{x ^{2} + 19}

Simplify

\frac{1}{x ^{2} + 19} \cdot \frac{x}{x ^{2} + 19} : \frac{x}{x ^{2} + 19}

= \frac{x}{x ^{2} + 19}

What is the derivative of ln(sqrt(x^2+19)) ?
The derivative of ln(sqrt(x^2+19)) is x/(x^2+19)
What is the first derivative of ln(sqrt(x^2+19)) ?
The first derivative of ln(sqrt(x^2+19)) is x/(x^2+19)