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

The derivative of 3/(2-3x) is 9/((2-3x)^2)

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

The first derivative of 3/(2-3x) is 9/((2-3x)^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}{2 - 3 x})

\frac{9}{( 2 - 3 x ) ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

3 (- \frac{1}{( 2 - 3 x ) ^{2}} (- 3)) : \frac{9}{( 2 - 3 x ) ^{2}}

= \frac{9}{( 2 - 3 x ) ^{2}}

What is the derivative of 3/(2-3x) ?
The derivative of 3/(2-3x) is 9/((2-3x)^2)
What is the first derivative of 3/(2-3x) ?
The first derivative of 3/(2-3x) is 9/((2-3x)^2)