What is the derivative of (-ln(1-6x)/x) ?

The derivative of (-ln(1-6x)/x) is -(-6x-ln(1-6x)(1-6x))/(x^2(1-6x))

What is the first derivative of (-ln(1-6x)/x) ?

The first derivative of (-ln(1-6x)/x) is -(-6x-ln(1-6x)(1-6x))/(x^2(1-6x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{- ln ( 1 - 6 x )}{x})

- \frac{- 6 x - ln ( 1 - 6 x ) ( 1 - 6 x )}{x ^{2} ( 1 - 6 x )}

Solution steps

\frac{d}{d x} (\frac{- ln ( 1 - 6 x )}{x})

Simplify

\frac{- ln ( 1 - 6 x )}{x} : - \frac{ln ( 1 - 6 x )}{x}

= \frac{d}{d x} (- \frac{ln ( 1 - 6 x )}{x})

Take the constant out:

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

= - \frac{d}{d x} (\frac{ln ( 1 - 6 x )}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - \frac{\frac{d}{d x} ( ln ( 1 - 6 x ) ) x - \frac{d x}{d x} ln ( 1 - 6 x )}{x ^{2}}

\frac{d}{d x} (ln (1 - 6 x)) = - \frac{6}{1 - 6 x}

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

= - \frac{( - \frac{6}{1 - 6 x} ) x - 1 \cdot ln ( 1 - 6 x )}{x ^{2}}

Simplify

- \frac{( - \frac{6}{1 - 6 x} ) x - 1 \cdot ln ( 1 - 6 x )}{x ^{2}} : - \frac{- 6 x - ln ( 1 - 6 x ) ( 1 - 6 x )}{x ^{2} ( 1 - 6 x )}

= - \frac{- 6 x - ln ( 1 - 6 x ) ( 1 - 6 x )}{x ^{2} ( 1 - 6 x )}

\frac{d}{d x} (x^{e} + e^{x})

\frac{d}{d x} (7 x y)

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

\int x 1 + 3 x d x

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

What is the derivative of (-ln(1-6x)/x) ?
The derivative of (-ln(1-6x)/x) is -(-6x-ln(1-6x)(1-6x))/(x^2(1-6x))
What is the first derivative of (-ln(1-6x)/x) ?
The first derivative of (-ln(1-6x)/x) is -(-6x-ln(1-6x)(1-6x))/(x^2(1-6x))