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Derivative of:
Derivative of e^(5*x)
Derivative of x^2+x+1
Derivative of (x^2+1)^2
Derivative of e^(1/x)
Integral of d{x}:
e^(5*x)
Graphing y =:
e^(5*x)
Limit of the function:
e^(5*x)
Identical expressions
e^(five *x)
e to the power of (5 multiply by x)
e to the power of (five multiply by x)
e(5*x)
e5*x
e^(5x)
e(5x)
e5x
e^5x
Similar expressions
y=(e^5x-1)/(3x^2*√x)
y=xtgx+lncosx+x+e^(5x)
y=e^(5x)⋅(3x+4).

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

Derivative of e^(5*x)

The solution

You have entered [src]

 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^(5*x)