Derivative of 5^6^x

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 / x\
 \6 /
5

$$5^{6^{x}}$$

5^(6^x)

Detail solution

Let $u = 6^{x}$ .
$\frac{d}{d u} 5^{u} = 5^{u} \log{\left(5 \right)}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} 6^{x}$ :
1. $\frac{d}{d x} 6^{x} = 6^{x} \log{\left(6 \right)}$
The result of the chain rule is:

$5^{6^{x}} 6^{x} \log{\left(5 \right)} \log{\left(6 \right)}$

The answer is:

$5^{6^{x}} 6^{x} \log{\left(5 \right)} \log{\left(6 \right)}$

The first derivative [src]

 / x\                 
 \6 /  x              
5    *6 *log(5)*log(6)

$$5^{6^{x}} 6^{x} \log{\left(5 \right)} \log{\left(6 \right)}$$

Simplify

The second derivative [src]

 / x\                                  
 \6 /  x    2    /     x       \       
5    *6 *log (6)*\1 + 6 *log(5)/*log(5)

$$5^{6^{x}} 6^{x} \left(6^{x} \log{\left(5 \right)} + 1\right) \log{\left(5 \right)} \log{\left(6 \right)}^{2}$$

Simplify

The third derivative [src]

 / x\                                                   
 \6 /  x    3    /     2*x    2         x       \       
5    *6 *log (6)*\1 + 6   *log (5) + 3*6 *log(5)/*log(5)

$$5^{6^{x}} 6^{x} \left(6^{2 x} \log{\left(5 \right)}^{2} + 3 \cdot 6^{x} \log{\left(5 \right)} + 1\right) \log{\left(5 \right)} \log{\left(6 \right)}^{3}$$

Simplify

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Derivative of 5^6^x

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