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(x^2+2x)e^x

Derivative of (x^2+2x)e^x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
/ 2      \  x
\x  + 2*x/*e 
$$\left(x^{2} + 2 x\right) e^{x}$$
d // 2      \  x\
--\\x  + 2*x/*e /
dx               
$$\frac{d}{d x} \left(x^{2} + 2 x\right) e^{x}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result is:

    ; to find :

    1. The derivative of is itself.

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
           x   / 2      \  x
(2 + 2*x)*e  + \x  + 2*x/*e 
$$\left(2 x + 2\right) e^{x} + \left(x^{2} + 2 x\right) e^{x}$$
The second derivative [src]
                       x
(6 + 4*x + x*(2 + x))*e 
$$\left(x \left(x + 2\right) + 4 x + 6\right) e^{x}$$
The third derivative [src]
                        x
(12 + 6*x + x*(2 + x))*e 
$$\left(x \left(x + 2\right) + 6 x + 12\right) e^{x}$$
The graph
Derivative of (x^2+2x)e^x