What is (\partial)/(\partial x)(ln(y/x)) ?

The answer to (\partial)/(\partial x)(ln(y/x)) is -1/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(ln(y/x))

\frac{\partial}{\partial x} (ln (\frac{y}{x}))

- \frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (\frac{y}{x}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{\frac{y}{x}} \frac{\partial}{\partial x} (\frac{y}{x})

= \frac{1}{\frac{y}{x}} \frac{\partial}{\partial x} (\frac{y}{x})

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

= \frac{1}{\frac{y}{x}} (- \frac{y}{x ^{2}})

Simplify

\frac{1}{\frac{y}{x}} (- \frac{y}{x ^{2}}) : - \frac{1}{x}

= - \frac{1}{x}

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

n = 1 \sum \infty \frac{3 ^{n}}{5 ^{n}}

\int x (x - 2)^{3} d x

f (x) = 3 + 4 x^{2} - 2 x^{3}, (2, 3)

\int (1 - x^{2})^{3} d x

What is (\partial)/(\partial x)(ln(y/x)) ?
The answer to (\partial)/(\partial x)(ln(y/x)) is -1/x