What is the derivative of x/(1-ln(x-5)) ?

The derivative of x/(1-ln(x-5)) is (2x-ln(x-5)(x-5)-5)/((x-5)(1-ln(x-5))^2)

What is the first derivative of x/(1-ln(x-5)) ?

The first derivative of x/(1-ln(x-5)) is (2x-ln(x-5)(x-5)-5)/((x-5)(1-ln(x-5))^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{x}{1 - ln ( x - 5 )}

\frac{2 x - ln ( x - 5 ) ( x - 5 ) - 5}{( x - 5 ) ( 1 - ln ( x - 5 ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{1 - ln ( x - 5 )})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 1 - ln ( x - 5 ) ) - \frac{d}{d x} ( 1 - ln ( x - 5 ) ) x}{( 1 - ln ( x - 5 ) ) ^{2}}

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

\frac{d}{d x} (1 - ln (x - 5)) = - \frac{1}{x - 5}

= \frac{1 \cdot ( 1 - ln ( x - 5 ) ) - ( - \frac{1}{x - 5} ) x}{( 1 - ln ( x - 5 ) ) ^{2}}

Simplify

\frac{1 \cdot ( 1 - ln ( x - 5 ) ) - ( - \frac{1}{x - 5} ) x}{( 1 - ln ( x - 5 ) ) ^{2}} : \frac{2 x - ln ( x - 5 ) ( x - 5 ) - 5}{( x - 5 ) ( 1 - ln ( x - 5 ) ) ^{2}}

= \frac{2 x - ln ( x - 5 ) ( x - 5 ) - 5}{( x - 5 ) ( 1 - ln ( x - 5 ) ) ^{2}}

\int_{0}^{\frac{5 π}{4}} 3 tan (\frac{x}{5}) d x

n = 0 \sum \infty \frac{1}{n ^{2} + 1}

\frac{d y}{d x}, y = 7^{x}

n = 0 \sum \infty \frac{1 ^{n}}{4 ^{n}}

(3 x - 2)^{^{'}}

What is the derivative of x/(1-ln(x-5)) ?
The derivative of x/(1-ln(x-5)) is (2x-ln(x-5)(x-5)-5)/((x-5)(1-ln(x-5))^2)
What is the first derivative of x/(1-ln(x-5)) ?
The first derivative of x/(1-ln(x-5)) is (2x-ln(x-5)(x-5)-5)/((x-5)(1-ln(x-5))^2)