Derivative of y=loge^x

You have entered [src]

   x   
log (E)

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

log(E)^x

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 graph

Plot the graph f(x)

Plot the graph f'(x)

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

The graph