Производная log(5)^x

Вы ввели

   x   
log (5)

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

d /   x   \
--\log (5)/
dx         

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

Подробное решение

1. $\frac{d}{d x} \log{\left(5 \right)}^{x} = \log{\left(5 \right)}^{x} \log{\left(\log{\left(5 \right)} \right)}$

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Ответ:

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

Первая производная

   x               
log (5)*log(log(5))

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

Вторая производная

   x       2        
log (5)*log (log(5))

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

Третья производная

   x       3        
log (5)*log (log(5))

$$\log{\left(5 \right)}^{x} \log{\left(\log{\left(5 \right)} \right)}^{3}$$

График