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e^(3x)^2

Derivative of 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) /
e        
$$e^{\left(3 x\right)^{2}}$$
  / /     2\\
d | \(3*x) /|
--\e        /
dx           
$$\frac{d}{d x} e^{\left(3 x\right)^{2}}$$
Detail solution
  1. Let .

  2. The derivative of is itself.

  3. Then, apply the chain rule. Multiply by :

    1. Let .

    2. Apply the power rule: goes to

    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 of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
      /     2\
      \(3*x) /
18*x*e        
$$18 x e^{\left(3 x\right)^{2}}$$
The second derivative [src]
                /     2\
   /        2\  \(3*x) /
18*\1 + 18*x /*e        
$$18 \cdot \left(18 x^{2} + 1\right) e^{\left(3 x\right)^{2}}$$
The third derivative [src]
                  /     2\
      /       2\  \(3*x) /
972*x*\1 + 6*x /*e        
$$972 x \left(6 x^{2} + 1\right) e^{\left(3 x\right)^{2}}$$
The graph
Derivative of e^(3x)^2