Calculus Examples

$y = 5^{x}$

Step 1

Set $y$ as a function of $x$ .

$f (x) = 5^{x}$

Step 2

Differentiate using the Exponential Rule which states that $\frac{d}{d x} [a^{x}]$ is $a^{x} \ln (a)$ where $a$ = $5$ .

$5^{x} \ln (5)$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution

Step 4

There are no solution found by setting the derivative equal to $0$ , $5^{x} \ln (5) = 0$ so there are no horizontal tangent lines.

No horizontal tangent lines found

Step 5