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Derivative of:
Derivative of 5x^3
Derivative of 4*sqrt(x)
Derivative of 10x
Derivative of x*ctgx
Identical expressions
С*e^(3x^ two)
С multiply by e to the power of (3x squared )
С multiply by e to the power of (3x to the power of two)
С*e(3x2)
С*e3x2
С*e^(3x²)
С*e to the power of (3x to the power of 2)
Сe^(3x^2)
Сe(3x2)
Сe3x2
Сe^3x^2

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

Derivative of С*e^(3x^2)

The solution

You have entered [src]

      2
   3*x 
c*e

$$c e^{3 x^{2}}$$

  /      2\
d |   3*x |
--\c*e    /
dx

$$\frac{\partial}{\partial x} c e^{3 x^{2}}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 3 x^{2}$ .
2. The derivative of $e^{u}$ is itself.
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 3 x^{2}$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $6 x$
  The result of the chain rule is:
  
  $6 x e^{3 x^{2}}$
So, the result is: $6 c x e^{3 x^{2}}$

The answer is:

$6 c x e^{3 x^{2}}$

The first derivative [src]

          2
       3*x 
6*c*x*e

$$6 c x e^{3 x^{2}}$$

Simplify

The second derivative [src]

                   2
    /       2\  3*x 
6*c*\1 + 6*x /*e

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

Simplify

The third derivative [src]

                       2
        /       2\  3*x 
108*c*x*\1 + 2*x /*e

$$108 c x \left(2 x^{2} + 1\right) e^{3 x^{2}}$$

Simplify