Calculus Examples

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

Step 1

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

$e^{x}$

Step 2

Set the derivative equal to $0$ then solve the equation $e^{x} = 0$ .

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Step 2.1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{x}) = \ln (0)$

Step 2.2

The equation cannot be solved because $\ln (0)$ is undefined.

Undefined

Step 2.3

There is no solution for $e^{x} = 0$

No solution

Step 3

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

No horizontal tangent lines found

Step 4