Derivative of 4^x+1

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 x    
4  + 1

$$4^{x} + 1$$

4^x + 1

Detail solution

Differentiate $4^{x} + 1$ term by term:
1. $\frac{d}{d x} 4^{x} = 4^{x} \log{\left(4 \right)}$
2. The derivative of the constant $1$ is zero.
The result is: $4^{x} \log{\left(4 \right)}$
Now simplify:

$\log{\left(4^{4^{x}} \right)}$

The answer is:

$\log{\left(4^{4^{x}} \right)}$

The graph

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The first derivative [src]

 x       
4 *log(4)

$$4^{x} \log{\left(4 \right)}$$

Simplify

The second derivative [src]

 x    2   
4 *log (4)

$$4^{x} \log{\left(4 \right)}^{2}$$

Simplify

The third derivative [src]

 x    3   
4 *log (4)

$$4^{x} \log{\left(4 \right)}^{3}$$

Simplify

The graph