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Derivative of:
Derivative of t-sint
Derivative of -3*x^3+2*x^2-x-5
Derivative of (x+5)/(x-1)
Derivative of x^4/(x+1)^3
Integral of d{x}:
e^(x/3)
Limit of the function:
e^(x/3)
Identical expressions
e^(x/ three)
e to the power of (x divide by 3)
e to the power of (x divide by three)
e(x/3)
ex/3
e^x/3
e^(x divide by 3)

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

Derivative of e^(x/3)

The solution

You have entered [src]

 x
 -
 3
E

e^{\frac{x}{3}}

E^(x/3)

Detail solution

Let $u = \frac{x}{3}$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{x}{3}$ :
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: $\frac{1}{3}$
The result of the chain rule is:

$\frac{e^{\frac{x}{3}}}{3}$
Now simplify:

$\frac{e^{\frac{x}{3}}}{3}$

The answer is:

\frac{e^{\frac{x}{3}}}{3}

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 x
 -
 3
e 
--
3

\frac{e^{\frac{x}{3}}}{3}

Simplify

The second derivative [src]

 x
 -
 3
e 
--
9

\frac{e^{\frac{x}{3}}}{9}

Simplify

The third derivative [src]

 x
 -
 3
e 
--
27

\frac{e^{\frac{x}{3}}}{27}

Simplify

The graph

Derivative of e^(x/3)