Derivative of 2^log(x)

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 log(x)
2

$$2^{\log{\left(x \right)}}$$

2^log(x)

Detail solution

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

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

The answer is:

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

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The first derivative [src]

 log(x)       
2      *log(2)
--------------
      x

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

Simplify

The second derivative [src]

 log(x)                     
2      *(-1 + log(2))*log(2)
----------------------------
              2             
             x

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

Simplify

The third derivative [src]

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

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

Simplify

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Identical expressions

Derivative of 2^log(x)

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