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

Derivative of e^(2x)

The solution

You have entered [src]

 2*x
e

$$e^{2 x}$$

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

$$\frac{d}{d x} e^{2 x}$$

Transform

Detail solution

Let $u = 2 x$ .
The derivative of $e^{u}$ is itself.
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:

$2 e^{2 x}$

The answer is:

$2 e^{2 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2*x
2*e

$$2 e^{2 x}$$

Simplify

The second derivative [src]

   2*x
4*e

$$4 e^{2 x}$$

Simplify

The third derivative [src]

   2*x
8*e

$$8 e^{2 x}$$

Simplify

The graph

Derivative of e^(2x)