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Derivative of:
Derivative of 5-7x
Derivative of sqrt(x-1)/(sqrt(x^2-x)-1)
Derivative of 3*x^2-1/x^3
Derivative of 3^(1/x)
Integral of d{x}:
3^(1/x)
Graphing y =:
3^(1/x)
Limit of the function:
3^(1/x)
Identical expressions
three ^(one /x)
3 to the power of (1 divide by x)
three to the power of (one divide by x)
3(1/x)
31/x
3^1/x
3^(1 divide by x)

The derivative of the function/ 3^(1/x)

Derivative of 3^(1/x)

The solution

You have entered [src]

x ___
\/ 3

$$3^{\frac{1}{x}}$$

3^(1/x)

Detail solution

Let $u = \frac{1}{x}$ .
$\frac{d}{d u} 3^{u} = 3^{u} \log{\left(3 \right)}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{1}{x}$ :
1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
The result of the chain rule is:

$- \frac{3^{\frac{1}{x}} \log{\left(3 \right)}}{x^{2}}$

The answer is:

$- \frac{3^{\frac{1}{x}} \log{\left(3 \right)}}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 x ___        
-\/ 3 *log(3) 
--------------
       2      
      x

$$- \frac{3^{\frac{1}{x}} \log{\left(3 \right)}}{x^{2}}$$

Simplify

The second derivative [src]

x ___ /    log(3)\       
\/ 3 *|2 + ------|*log(3)
      \      x   /       
-------------------------
             3           
            x

$$\frac{3^{\frac{1}{x}} \left(2 + \frac{\log{\left(3 \right)}}{x}\right) \log{\left(3 \right)}}{x^{3}}$$

Simplify

The third derivative [src]

       /       2              \        
 x ___ |    log (3)   6*log(3)|        
-\/ 3 *|6 + ------- + --------|*log(3) 
       |        2        x    |        
       \       x              /        
---------------------------------------
                    4                  
                   x

$$- \frac{3^{\frac{1}{x}} \left(6 + \frac{6 \log{\left(3 \right)}}{x} + \frac{\log{\left(3 \right)}^{2}}{x^{2}}\right) \log{\left(3 \right)}}{x^{4}}$$

Simplify

The graph

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Identical expressions

Derivative of 3^(1/x)

The graph:

Piecewise:

The solution