Mister Exam

Lang:

Derivative of 2^x+e^x

You have entered [src]

 x    x
2  + E

$$2^{x} + e^{x}$$

2^x + E^x

Detail solution

Differentiate $2^{x} + e^{x}$ term by term:
1. $\frac{d}{d x} 2^{x} = 2^{x} \log{\left(2 \right)}$
2. The derivative of $e^{x}$ is itself.
The result is: $2^{x} \log{\left(2 \right)} + e^{x}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 x    x       
E  + 2 *log(2)

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

Simplify

The second derivative [src]

 x    2       x
2 *log (2) + e

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

Simplify

The third derivative [src]

 x    3       x
2 *log (2) + e

$$2^{x} \log{\left(2 \right)}^{3} + e^{x}$$

Simplify

The graph