What is the derivative of ln(x^2+14x+55) ?

The derivative of ln(x^2+14x+55) is (2x+14)/(x^2+14x+55)

What is the first derivative of ln(x^2+14x+55) ?

The first derivative of ln(x^2+14x+55) is (2x+14)/(x^2+14x+55)

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} + 14 x + 55))

\frac{2 x + 14}{x ^{2} + 14 x + 55}

Solution steps

\frac{d}{d x} (ln (x^{2} + 14 x + 55))

Apply the chain rule:

\frac{1}{x ^{2} + 14 x + 55} \frac{d}{d x} (x^{2} + 14 x + 55)

= \frac{1}{x ^{2} + 14 x + 55} \frac{d}{d x} (x^{2} + 14 x + 55)

\frac{d}{d x} (x^{2} + 14 x + 55) = 2 x + 14

= \frac{1}{x ^{2} + 14 x + 55} (2 x + 14)

Simplify

\frac{1}{x ^{2} + 14 x + 55} (2 x + 14) : \frac{2 x + 14}{x ^{2} + 14 x + 55}

= \frac{2 x + 14}{x ^{2} + 14 x + 55}

What is the derivative of ln(x^2+14x+55) ?
The derivative of ln(x^2+14x+55) is (2x+14)/(x^2+14x+55)
What is the first derivative of ln(x^2+14x+55) ?
The first derivative of ln(x^2+14x+55) is (2x+14)/(x^2+14x+55)