Mister Exam

Derivative of xe^(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   x
x*E 
exxe^{x} x
x*E^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: ex+xexe^{x} + 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
The first derivative [src]
 x      x
E  + x*e 
ex+xexe^{x} + x e^{x}
The second derivative [src]
         x
(2 + x)*e 
(x+2)ex\left(x + 2\right) e^{x}
The third derivative [src]
         x
(3 + x)*e 
(x+3)ex\left(x + 3\right) e^{x}
The graph
Derivative of xe^(x)