Derivative of loga^x

You have entered [src]

   x   
log (a)

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

log(a)^x

Detail solution

$\frac{\partial}{\partial x} \log{\left(a \right)}^{x} = \log{\left(a \right)}^{x} \log{\left(\log{\left(a \right)} \right)}$

The answer is:

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

The first derivative [src]

   x               
log (a)*log(log(a))

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

Simplify

The second derivative [src]

   x       2        
log (a)*log (log(a))

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

Simplify

The third derivative [src]

   x       3        
log (a)*log (log(a))

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

Simplify