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x^e
The derivative of the function/ x^e

Derivative of x^e

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 E
x
$$x^{e}$$ 
x^E
Detail solution

  1. Apply the power rule: goes to

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   E
E*x 
----
 x
$$\frac{e x^{e}}{x}$$
Simplify
The second derivative [src] 
   E         
E*x *(-1 + E)
-------------
       2     
      x
$$\frac{e x^{e} \left(-1 + e\right)}{x^{2}}$$
Simplify
The third derivative [src] 
   E /           2\
E*x *\2 - 3*E + e /
-------------------
          3        
         x
$$\frac{e x^{e} \left(- 3 e + 2 + e^{2}\right)}{x^{3}}$$
Simplify
The graph
Derivative of x^e
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