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

The derivative of ln(x+2y) is (1+2\frac{dy)/(dx)}{x+2y}

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

The first derivative of ln(x+2y) is (1+2\frac{dy)/(dx)}{x+2y}

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 y))

\frac{1 + 2 \frac{d y}{d x}}{x + 2 y}

Solution steps

\frac{d}{d x} (ln (x + 2 y))

Apply the chain rule:

\frac{1}{x + 2 y} \frac{d}{d x} (x + 2 y)

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

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

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

Simplify

\frac{1}{x + 2 y} (1 + 2 \frac{d y}{d x}) : \frac{1 + 2 \frac{d y}{d x}}{x + 2 y}

= \frac{1 + 2 \frac{d y}{d x}}{x + 2 y}

What is the derivative of ln(x+2y) ?
The derivative of ln(x+2y) is (1+2\frac{dy)/(dx)}{x+2y}
What is the first derivative of ln(x+2y) ?
The first derivative of ln(x+2y) is (1+2\frac{dy)/(dx)}{x+2y}