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x^(1/3)*e^(-x)
The derivative of the function/ x^(1/3)*e^(-x)

Derivative of x^(1/3)*e^(-x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
3 ___  -x
\/ x *e
$$\sqrt[3]{x} e^{- x}$$ 
d /3 ___  -x\
--\\/ x *e  /
dx
$$\frac{d}{d x} \sqrt[3]{x} e^{- x}$$
Transform
Detail solution

  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the power rule: goes to

    To find :

    1. The derivative of is itself.

    Now plug in to the quotient rule:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                -x  
  3 ___  -x    e    
- \/ x *e   + ------
                 2/3
              3*x
$$- \sqrt[3]{x} e^{- x} + \frac{e^{- x}}{3 x^{\frac{2}{3}}}$$
Simplify
The second derivative [src] 
/3 ___     2        2   \  -x
|\/ x  - ------ - ------|*e  
|           2/3      5/3|    
\        3*x      9*x   /
$$\left(\sqrt[3]{x} - \frac{2}{3 x^{\frac{2}{3}}} - \frac{2}{9 x^{\frac{5}{3}}}\right) e^{- x}$$
Simplify
The third derivative [src] 
/ 1     3 ___     2         10  \  -x
|---- - \/ x  + ------ + -------|*e  
| 2/3              5/3       8/3|    
\x              3*x      27*x   /
$$\left(- \sqrt[3]{x} + \frac{1}{x^{\frac{2}{3}}} + \frac{2}{3 x^{\frac{5}{3}}} + \frac{10}{27 x^{\frac{8}{3}}}\right) e^{- x}$$
Simplify
The graph
Derivative of x^(1/3)*e^(-x)
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