What is the derivative of x^{1/3}+(x-4)/(3x^{5/3)} ?

The derivative of x^{1/3}+(x-4)/(3x^{5/3)} is 1/(3x^{2/3)}+(2(-x+10))/(9x^{8/3)}

What is the first derivative of x^{1/3}+(x-4)/(3x^{5/3)} ?

The first derivative of x^{1/3}+(x-4)/(3x^{5/3)} is 1/(3x^{2/3)}+(2(-x+10))/(9x^{8/3)}

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derivative of

x^{\frac{1}{3}} + \frac{x - 4}{3 x ^{\frac{5}{3}}}

\frac{1}{3 x ^{\frac{2}{3}}} + \frac{2 ( - x + 10 )}{9 x ^{\frac{8}{3}}}

Solution steps

\frac{d}{d x} (x^{\frac{1}{3}} + \frac{x - 4}{3 x ^{\frac{5}{3}}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{\frac{1}{3}}) + \frac{d}{d x} (\frac{x - 4}{3 x ^{\frac{5}{3}}})

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

\frac{d}{d x} (\frac{x - 4}{3 x ^{\frac{5}{3}}}) = \frac{2 ( - x + 10 )}{9 x ^{\frac{8}{3}}}

= \frac{1}{3 x ^{\frac{2}{3}}} + \frac{2 ( - x + 10 )}{9 x ^{\frac{8}{3}}}

\frac{d}{d x} (- sin (x^{2} + 3) \cdot 2 x)

\int 5 x^{2} (2 x^{3} + 3)^{4} d x

\int \frac{( ln ( ln ( x ) ) )}{x} d x

\frac{\partial}{\partial y} (y e^{- x})

What is the derivative of x^{1/3}+(x-4)/(3x^{5/3)} ?
The derivative of x^{1/3}+(x-4)/(3x^{5/3)} is 1/(3x^{2/3)}+(2(-x+10))/(9x^{8/3)}
What is the first derivative of x^{1/3}+(x-4)/(3x^{5/3)} ?
The first derivative of x^{1/3}+(x-4)/(3x^{5/3)} is 1/(3x^{2/3)}+(2(-x+10))/(9x^{8/3)}