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x*e^(3*x)

Derivative of x*e^(3*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   3*x
x*E   
$$e^{3 x} x$$
x*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        3*x
E    + 3*x*e   
$$3 x e^{3 x} + e^{3 x}$$
The second derivative [src]
             3*x
3*(2 + 3*x)*e   
$$3 \left(3 x + 2\right) e^{3 x}$$
The third derivative [src]
            3*x
27*(1 + x)*e   
$$27 \left(x + 1\right) e^{3 x}$$
The graph
Derivative of x*e^(3*x)