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Derivative of С*e^(3x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
      2
   3*x 
c*e    
$$c e^{3 x^{2}}$$
  /      2\
d |   3*x |
--\c*e    /
dx         
$$\frac{\partial}{\partial x} c e^{3 x^{2}}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    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:

    So, the result is:


The answer is:

The first derivative [src]
          2
       3*x 
6*c*x*e    
$$6 c x e^{3 x^{2}}$$
The second derivative [src]
                   2
    /       2\  3*x 
6*c*\1 + 6*x /*e    
$$6 c \left(6 x^{2} + 1\right) e^{3 x^{2}}$$
The third derivative [src]
                       2
        /       2\  3*x 
108*c*x*\1 + 2*x /*e    
$$108 c x \left(2 x^{2} + 1\right) e^{3 x^{2}}$$