Calculus Examples

$x e^{- x} = 0$

Step 1

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 2

Set $x$ equal to $0$ .

$x = 0$

Step 3

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

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Step 3.1

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

$e^{- x} = 0$

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

Undefined

Step 3.2.3

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

No solution

Step 4

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

$x = 0$