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Derivative of:
Derivative of sin(2*x^2+3)
Derivative of 5*x^4-7*x^2-x
Derivative of 3/x^5
Derivative of 3*e^(2*x)
Integral of d{x}:
3*e^(2*x)
Identical expressions
three *e^(two *x)
3 multiply by e to the power of (2 multiply by x)
three multiply by e to the power of (two multiply by x)
3*e(2*x)
3*e2*x
3e^(2x)
3e(2x)
3e2x
3e^2x

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

Derivative of 3e^(2x)

The solution

You have entered [src]

   2*x
3*E

$$3 e^{2 x}$$

3*E^(2*x)

Detail solution

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

The answer is:

$6 e^{2 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2*x
6*e

$$6 e^{2 x}$$

Simplify

The second derivative [src]

    2*x
12*e

$$12 e^{2 x}$$

Simplify

The third derivative [src]

    2*x
24*e

$$24 e^{2 x}$$

Simplify

The graph

Derivative of 3*e^(2*x)