Calculus Examples

$0 = x e^{x}$

Step 1

Rewrite the equation as $x e^{x} = 0$ .

$x e^{x} = 0$

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$e^{x} = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $e^{x}$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $e^{x}$ equal to $0$ .

$e^{x} = 0$

Step 4.2

Solve $e^{x} = 0$ for $x$ .

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Step 4.2.1

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

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

Step 4.2.2

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

Undefined

Step 4.2.3

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

No solution

Step 5

The final solution is all the values that make $x e^{x} = 0$ true.

$x = 0$