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

Derivative of 3^(1/x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
x ___
\/ 3
31x3^{\frac{1}{x}} 
3^(1/x)
Detail solution

  1. Let u=1xu = \frac{1}{x}.

  2. ddu3u=3ulog⁡(3)\frac{d}{d u} 3^{u} = 3^{u} \log{\left(3 \right)}

  3. Then, apply the chain rule. Multiply by ddx1x\frac{d}{d x} \frac{1}{x}:

    1. Apply the power rule: 1x\frac{1}{x} goes to −1x2- \frac{1}{x^{2}}

    The result of the chain rule is:

    −31xlog⁡(3)x2- \frac{3^{\frac{1}{x}} \log{\left(3 \right)}}{x^{2}}

The answer is:

−31xlog⁡(3)x2- \frac{3^{\frac{1}{x}} \log{\left(3 \right)}}{x^{2}}

The graph
02468-8-6-4-2-1010-100000005000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 x ___        
-\/ 3 *log(3) 
--------------
       2      
      x
−31xlog⁡(3)x2- \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
31x(2+log⁡(3)x)log⁡(3)x3\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
−31x(6+6log⁡(3)x+log⁡(3)2x2)log⁡(3)x4- \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
Derivative of 3^(1/x)
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