What is the derivative of ((3x-1)/(x^{2/3)}) ?

The derivative of ((3x-1)/(x^{2/3)}) is (3x+2)/(3x^{5/3)}

What is the first derivative of ((3x-1)/(x^{2/3)}) ?

The first derivative of ((3x-1)/(x^{2/3)}) is (3x+2)/(3x^{5/3)}

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

\frac{3 x + 2}{3 x ^{\frac{5}{3}}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{3 x + 2}{3 x ^{\frac{5}{3}}}

\frac{\partial}{\partial x} (4 + x ln (x y - 5))

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

\int \frac{5 x}{e ^{2 x}} d x

\int \frac{7 x + 8}{7 x ^{2} + 16 x + 9} d x

\frac{d}{d x} (\frac{1}{x ^{11}})

What is the derivative of ((3x-1)/(x^{2/3)}) ?
The derivative of ((3x-1)/(x^{2/3)}) is (3x+2)/(3x^{5/3)}
What is the first derivative of ((3x-1)/(x^{2/3)}) ?
The first derivative of ((3x-1)/(x^{2/3)}) is (3x+2)/(3x^{5/3)}