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x*exp(x)
The derivative of the function/ x*exp(x)

Derivative of x*exp(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   x
x*e
xexx e^{x} 
x*exp(x)
Detail solution

  1. Apply the product rule:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

    f(x)=xf{\left(x \right)} = x; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the power rule: xx goes to 11

    g(x)=exg{\left(x \right)} = e^{x}; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. The derivative of exe^{x} is itself.

    The result is: xex+exx e^{x} + e^{x}

  2. Now simplify:

    (x+1)ex\left(x + 1\right) e^{x}

The answer is:

(x+1)ex\left(x + 1\right) e^{x}

The graph
02468-8-6-4-2-1010-250000250000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   x    x
x*e  + e
xex+exx e^{x} + e^{x}
Simplify
The second derivative [src] 
         x
(2 + x)*e
(x+2)ex\left(x + 2\right) e^{x}
Simplify
The third derivative [src] 
         x
(3 + x)*e
(x+3)ex\left(x + 3\right) e^{x}
Simplify
The graph
Derivative of x*exp(x)
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