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Derivative of:
Derivative of x^x^x
Derivative of x^-6
Derivative of x^-11
Derivative of -x/2
Identical expressions
e^(three *x)+ two
e to the power of (3 multiply by x) plus 2
e to the power of (three multiply by x) plus two
e(3*x)+2
e3*x+2
e^(3x)+2
e(3x)+2
e3x+2
e^3x+2
Similar expressions
e^(3*x)-2

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

Derivative of e^(3*x)+2

The solution

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 3*x    
e    + 2

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

d / 3*x    \
--\e    + 2/
dx

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

Transform

Detail solution

Differentiate $e^{3 x} + 2$ term by term:
1. Let $u = 3 x$ .
2. The derivative of $e^{u}$ is itself.
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:
  
  $3 e^{3 x}$
4. The derivative of the constant $2$ is zero.
The result is: $3 e^{3 x}$

The answer is:

$3 e^{3 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   3*x
3*e

$$3 e^{3 x}$$

Simplify

The second derivative [src]

   3*x
9*e

$$9 e^{3 x}$$

Simplify

The third derivative [src]

    3*x
27*e

$$27 e^{3 x}$$

Simplify

The graph

Derivative of e^(3*x)+2