What is (\partial)/(\partial x)(-1/2 ln(x/a)) ?

The answer to (\partial)/(\partial x)(-1/2 ln(x/a)) is -1/(2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(-1/2 ln(x/a))

\frac{\partial}{\partial x} (- \frac{1}{2} ln (\frac{x}{a}))

- \frac{1}{2 x}

Solution steps

\frac{\partial}{\partial x} (- \frac{1}{2} ln (\frac{x}{a}))

Take the constant out:

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

= - \frac{1}{2} \frac{\partial}{\partial x} (ln (\frac{x}{a}))

Apply the chain rule:

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

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

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

= - \frac{1}{2} \cdot \frac{1}{\frac{x}{a}} \cdot \frac{1}{a}

Simplify

- \frac{1}{2} \cdot \frac{1}{\frac{x}{a}} \cdot \frac{1}{a} : - \frac{1}{2 x}

= - \frac{1}{2 x}

f (x) = x (x - 8), at x = 16

\int_{0}^{3} 6 y - 2 y^{2} d y

ln (2 + x)

- x + tan (x)

cos (\frac{1 - e ^{7 x}}{1 + e ^{7 x}})

What is (\partial)/(\partial x)(-1/2 ln(x/a)) ?
The answer to (\partial)/(\partial x)(-1/2 ln(x/a)) is -1/(2x)