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)}

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\frac{d}{d x} (\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}}}

\frac{\partial}{\partial y} (2 x + y^{3})

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

5 - x^{2}, sin (x), - 2.384677, 2.0252116

\int \frac{1 - sin ( x )}{cos ( x )} d x

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)}