What is the derivative of (4x+4)/(3x^{2/3)} ?

The derivative of (4x+4)/(3x^{2/3)} is (4x-8)/(9x^{5/3)}

What is the first derivative of (4x+4)/(3x^{2/3)} ?

The first derivative of (4x+4)/(3x^{2/3)} is (4x-8)/(9x^{5/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{4 x + 4}{3 x ^{\frac{2}{3}}}

\frac{4 x - 8}{9 x ^{\frac{5}{3}}}

Solution steps

\frac{d}{d x} (\frac{4 x + 4}{3 x ^{\frac{2}{3}}})

Take the constant out:

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

= \frac{1}{3} \frac{d}{d x} (\frac{4 x + 4}{x ^{\frac{2}{3}}})

Apply the Quotient Rule:

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

= \frac{1}{3} \cdot \frac{\frac{d}{d x} ( 4 x + 4 ) x ^{\frac{2}{3}} - \frac{d}{d x} ( x ^{\frac{2}{3}} ) ( 4 x + 4 )}{( x ^{\frac{2}{3}} ) ^{2}}

\frac{d}{d x} (4 x + 4) = 4

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

= \frac{1}{3} \cdot \frac{4 x ^{\frac{2}{3}} - \frac{2}{3 x ^{\frac{1}{3}}} ( 4 x + 4 )}{( x ^{\frac{2}{3}} ) ^{2}}

Simplify

\frac{1}{3} \cdot \frac{4 x ^{\frac{2}{3}} - \frac{2}{3 x ^{\frac{1}{3}}} ( 4 x + 4 )}{( x ^{\frac{2}{3}} ) ^{2}} : \frac{4 x - 8}{9 x ^{\frac{5}{3}}}

= \frac{4 x - 8}{9 x ^{\frac{5}{3}}}

What is the derivative of (4x+4)/(3x^{2/3)} ?
The derivative of (4x+4)/(3x^{2/3)} is (4x-8)/(9x^{5/3)}
What is the first derivative of (4x+4)/(3x^{2/3)} ?
The first derivative of (4x+4)/(3x^{2/3)} is (4x-8)/(9x^{5/3)}