What is the derivative of ln(1/(x-y)) ?

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

What is the first derivative of ln(1/(x-y)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (ln (\frac{1}{x - y}))

- \frac{1 - \frac{d y}{d x}}{x - y}

Solution steps

\frac{d}{d x} (ln (\frac{1}{x - y}))

Simplify

ln (\frac{1}{x - y}) : - ln (x - y)

= \frac{d}{d x} (- ln (x - y))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (ln (x - y))

Apply the chain rule:

\frac{1}{x - y} \frac{d}{d x} (x - y)

= \frac{1}{x - y} \frac{d}{d x} (x - y)

\frac{d}{d x} (x - y) = 1 - \frac{d y}{d x}

= - \frac{1}{x - y} (1 - \frac{d y}{d x})

Simplify

- \frac{1}{x - y} (1 - \frac{d y}{d x}) : - \frac{1 - \frac{d y}{d x}}{x - y}

= - \frac{1 - \frac{d y}{d x}}{x - y}

\int \frac{2 x + 11}{x ^{2} + x - 6} d x

\int \frac{1}{x ^{2}} cos (\frac{1}{x}) d x

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 2})

\frac{\partial}{\partial x} ((6 - x - y)^{2})

\frac{d y}{d t} = - 2 (y - 3)

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