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

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   
$$x^{2} e^{2 x}$$
x^2*exp(2*x)
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. 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 of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
     2*x      2  2*x
2*x*e    + 2*x *e   
$$2 x^{2} e^{2 x} + 2 x e^{2 x}$$
The second derivative [src]
  /       2      \  2*x
2*\1 + 2*x  + 4*x/*e   
$$2 \left(2 x^{2} + 4 x + 1\right) e^{2 x}$$
50-я производная [src]
                /          2        \  2*x
562949953421312*\1225 + 2*x  + 100*x/*e   
$$562949953421312 \left(2 x^{2} + 100 x + 1225\right) e^{2 x}$$
The third derivative [src]
  /       2      \  2*x
4*\3 + 2*x  + 6*x/*e   
$$4 \left(2 x^{2} + 6 x + 3\right) e^{2 x}$$