Mister Exam

Lang:

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

Derivative of e^(3x)

The solution

You have entered [src]

 3*x
E

$$e^{3 x}$$

E^(3*x)

Detail solution

Let $u = 3 x$ .
The derivative of $e^{u}$ is itself.
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:

$3 e^{3 x}$

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^(3x)