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Derivative of:
Derivative of atan(sqrt(x))
Derivative of 3*x^5
Derivative of 3*x^2*e^x
Derivative of 3*cos(3*x)
Integral of d{x}:
e^(a*x)
Sum of series:
e^(a*x)
Limit of the function:
e^(a*x)
Identical expressions
e^(a*x)
e to the power of (a multiply by x)
e(a*x)
ea*x
e^(ax)
e(ax)
eax
e^ax
Similar expressions
e^(ax)

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

Derivative of e^(a*x)

The solution

You have entered [src]

 a*x
E

$$e^{a x}$$

E^(a*x)

Detail solution

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

$a e^{a x}$

The answer is:

$a e^{a x}$

The first derivative [src]

   a*x
a*e

$$a e^{a x}$$

Simplify

The second derivative [src]

 2  a*x
a *e

$$a^{2} e^{a x}$$

Simplify

The third derivative [src]

 3  a*x
a *e

$$a^{3} e^{a x}$$

Simplify