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(x^2)*e^(3x)

Derivative of (x^2)*e^(3x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2  3*x
x *e   
$$x^{2} e^{3 x}$$
d / 2  3*x\
--\x *e   /
dx         
$$\frac{d}{d x} x^{2} e^{3 x}$$
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]
     3*x      2  3*x
2*x*e    + 3*x *e   
$$3 x^{2} e^{3 x} + 2 x e^{3 x}$$
The second derivative [src]
/       2       \  3*x
\2 + 9*x  + 12*x/*e   
$$\left(9 x^{2} + 12 x + 2\right) e^{3 x}$$
The third derivative [src]
  /       2      \  3*x
9*\2 + 3*x  + 6*x/*e   
$$9 \cdot \left(3 x^{2} + 6 x + 2\right) e^{3 x}$$
3-th derivative [src]
  /       2      \  3*x
9*\2 + 3*x  + 6*x/*e   
$$9 \cdot \left(3 x^{2} + 6 x + 2\right) e^{3 x}$$
The graph
Derivative of (x^2)*e^(3x)