Derivative of loge^x

You have entered [src]

   x   
log (e)

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

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

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

Transform

Detail solution

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

$0$

The answer is:

$0$

The first derivative [src]

   x               
log (e)*log(log(e))

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

Simplify

The second derivative [src]

   x       2        
log (e)*log (log(e))

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

Simplify

The third derivative [src]

   x       3        
log (e)*log (log(e))

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

Simplify