Calculus Examples

y = 5^{x}

$y = 5^{x}$

Step 1

Set

y

$y$ as a function of

x

$x$ .

f (x) = 5^{x}

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

Step 2

Differentiate using the Exponential Rule which states that

\frac{d}{d x} [a^{x}]

$\frac{d}{d x} [a^{x}]$ is

a^{x} ln (a)

$a^{x} \ln (a)$ where

a

$a$ =

5

$5$ .

5^{x} ln (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

$0$ ,

5^{x} ln (5) = 0

$5^{x} \ln (5) = 0$ so there are no horizontal tangent lines.

No horizontal tangent lines found

Step 5