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Derivative of xexp(x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   / 2\
   \x /
x*e    
$$x e^{x^{2}}$$
x*exp(x^2)
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. Let .

    2. The derivative of is itself.

    3. Then, apply the chain rule. Multiply by :

      1. Apply the power rule: goes to

      The result of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
      / 2\    / 2\
   2  \x /    \x /
2*x *e     + e    
$$2 x^{2} e^{x^{2}} + e^{x^{2}}$$
The second derivative [src]
                / 2\
    /       2\  \x /
2*x*\3 + 2*x /*e    
$$2 x \left(2 x^{2} + 3\right) e^{x^{2}}$$
The third derivative [src]
                                / 2\
  /       2      2 /       2\\  \x /
2*\3 + 6*x  + 2*x *\3 + 2*x //*e    
$$2 \left(2 x^{2} \left(2 x^{2} + 3\right) + 6 x^{2} + 3\right) e^{x^{2}}$$