Find the Function f(x)=3^x

$f (x) = 3^{x}$

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 $3^{x}$ with respect to $x$ is $\frac{3^{x}}{\ln (3)}$ .

$\frac{3^{x}}{\ln (3)} + C$

Step 3

Rewrite $\frac{3^{x}}{\ln (3)} + C$ as $\frac{1}{\ln (3)} \cdot 3^{x} + C$ .

$\frac{1}{\ln (3)} \cdot 3^{x} + C$

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.

$F (x) = \frac{1}{\ln (3)} \cdot 3^{x} + C$