Derivative of log8^x

You have entered [src]

   x   
log (8)

$$\log{\left(8 \right)}^{x}$$

log(8)^x

Detail solution

$\frac{d}{d x} \log{\left(8 \right)}^{x} = \log{\left(8 \right)}^{x} \log{\left(\log{\left(8 \right)} \right)}$
Now simplify:

$\log{\left(\log{\left(8 \right)}^{\log{\left(8 \right)}^{x}} \right)}$

The answer is:

$\log{\left(\log{\left(8 \right)}^{\log{\left(8 \right)}^{x}} \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   x               
log (8)*log(log(8))

$$\log{\left(8 \right)}^{x} \log{\left(\log{\left(8 \right)} \right)}$$

Simplify

The second derivative [src]

   x       2        
log (8)*log (log(8))

$$\log{\left(8 \right)}^{x} \log{\left(\log{\left(8 \right)} \right)}^{2}$$

Simplify

The third derivative [src]

   x       3        
log (8)*log (log(8))

$$\log{\left(8 \right)}^{x} \log{\left(\log{\left(8 \right)} \right)}^{3}$$

Simplify