What is the derivative of ((3x-2)/(5x)) ?

The derivative of ((3x-2)/(5x)) is 2/(5x^2)

What is the first derivative of ((3x-2)/(5x)) ?

The first derivative of ((3x-2)/(5x)) is 2/(5x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{( 3 x - 2 )}{5 x})

\frac{2}{5 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{( 3 x - 2 )}{5 x})

Take the constant out:

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

= \frac{1}{5} \frac{d}{d x} (\frac{3 x - 2}{x})

Apply the Quotient Rule:

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

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( 3 x - 2 ) x - \frac{d x}{d x} ( 3 x - 2 )}{x ^{2}}

\frac{d}{d x} (3 x - 2) = 3

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

= \frac{1}{5} \cdot \frac{3 x - 1 \cdot ( 3 x - 2 )}{x ^{2}}

Simplify

\frac{1}{5} \cdot \frac{3 x - 1 \cdot ( 3 x - 2 )}{x ^{2}} : \frac{2}{5 x ^{2}}

= \frac{2}{5 x ^{2}}

What is the derivative of ((3x-2)/(5x)) ?
The derivative of ((3x-2)/(5x)) is 2/(5x^2)
What is the first derivative of ((3x-2)/(5x)) ?
The first derivative of ((3x-2)/(5x)) is 2/(5x^2)