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)}

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\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}}}

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)}