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Derivative of:
Derivative of x^-3
Derivative of x^2*e^x
Derivative of x^2*cos(x)
Derivative of 1/2*x^2
Identical expressions
e^(3x)^ two
e to the power of (3x) squared
e to the power of (3x) to the power of two
e(3x)2
e3x2
e^(3x)²
e to the power of (3x) to the power of 2
e^3x^2
Similar expressions
y=e^(3x^2)+1
y=e^((3*x^2-2x+1))

The derivative of the function/ e^(3x)^2

Derivative of e^(3x)^2

The solution

You have entered [src]

 /     2\
 \(3*x) /
e

$$e^{\left(3 x\right)^{2}}$$

  / /     2\\
d | \(3*x) /|
--\e        /
dx

$$\frac{d}{d x} e^{\left(3 x\right)^{2}}$$

Transform

Detail solution

Let $u = \left(3 x\right)^{2}$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x\right)^{2}$ :
1. Let $u = 3 x$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 3 x$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $3$
  The result of the chain rule is:
  
  $18 x$
The result of the chain rule is:

$18 x e^{\left(3 x\right)^{2}}$
Now simplify:

$18 x e^{9 x^{2}}$

The answer is:

$18 x e^{9 x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      /     2\
      \(3*x) /
18*x*e

$$18 x e^{\left(3 x\right)^{2}}$$

Simplify

The second derivative [src]

                /     2\
   /        2\  \(3*x) /
18*\1 + 18*x /*e

$$18 \cdot \left(18 x^{2} + 1\right) e^{\left(3 x\right)^{2}}$$

Simplify

The third derivative [src]

                  /     2\
      /       2\  \(3*x) /
972*x*\1 + 6*x /*e

$$972 x \left(6 x^{2} + 1\right) e^{\left(3 x\right)^{2}}$$

Simplify

The graph

Derivative of e^(3x)^2