Find the Function f(x)=4^x

$f (x) = 4^{x}$

Step 1

The function $F (x)$ can be found by evaluating the indefinite integral of the derivative $f (x)$ .

$F (x) = \int f (x) d x$

Step 2

The integral of $4^{x}$ with respect to $x$ is $\frac{4^{x}}{\ln (4)}$ .

$\frac{4^{x}}{\ln (4)} + C$

Step 3

Rewrite $\frac{4^{x}}{\ln (4)} + C$ as $\frac{1}{\ln (4)} \cdot 4^{x} + C$ .

$\frac{1}{\ln (4)} \cdot 4^{x} + C$

Step 4

The function $F$ if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.

$F (x) = \frac{1}{\ln (4)} \cdot 4^{x} + C$