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x^2*e^(x^2)

You entered:

x^2*e^(x^2)

What you mean?

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

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
    / 2\
 2  \x /
x *e    
$$x^{2} e^{x^{2}}$$
  /    / 2\\
d | 2  \x /|
--\x *e    /
dx          
$$\frac{d}{d x} x^{2} e^{x^{2}}$$
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\
     \x /      3  \x /
2*x*e     + 2*x *e    
$$2 x^{3} e^{x^{2}} + 2 x e^{x^{2}}$$
The second derivative [src]
                              / 2\
  /       2    2 /       2\\  \x /
2*\1 + 4*x  + x *\1 + 2*x //*e    
$$2 \left(x^{2} \cdot \left(2 x^{2} + 1\right) + 4 x^{2} + 1\right) e^{x^{2}}$$
The third derivative [src]
                                / 2\
    /       2    2 /       2\\  \x /
4*x*\6 + 6*x  + x *\3 + 2*x //*e    
$$4 x \left(x^{2} \cdot \left(2 x^{2} + 3\right) + 6 x^{2} + 6\right) e^{x^{2}}$$
The graph
Derivative of x^2*e^(x^2)