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e^x*log(x)
The derivative of the function/ e^x*log(x)

Derivative of e^x*log(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 x       
E *log(x)
$$e^{x} \log{\left(x \right)}$$ 
E^x*log(x)
Detail solution

  1. Apply the product rule:

    ; to find :

    1. The derivative of is itself.

    ; to find :

    1. The derivative of is .

    The result is:

  2. Now simplify:

The answer is:

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