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The derivative of the function/ e^(5x)

Derivative of e^(5x)

The solution

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 5*x
E

$$e^{5 x}$$

E^(5*x)

Detail solution

Let $u = 5 x$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} 5 x$ :
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: $5$
The result of the chain rule is:

$5 e^{5 x}$

The answer is:

$5 e^{5 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   5*x
5*e

$$5 e^{5 x}$$

Simplify

The second derivative [src]

    5*x
25*e

$$25 e^{5 x}$$

Simplify

The third derivative [src]

     5*x
125*e

$$125 e^{5 x}$$

Simplify

The graph

Derivative of e^(5x)