Calculus Examples

$- e^{\frac{1}{x}} = 0$

Step 1

Divide each term in $- e^{\frac{1}{x}} = 0$ by $- 1$ and simplify.

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Step 1.1

Divide each term in $- e^{\frac{1}{x}} = 0$ by $- 1$ .

$\frac{- e^{\frac{1}{x}}}{- 1} = \frac{0}{- 1}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Dividing two negative values results in a positive value.

$\frac{e^{\frac{1}{x}}}{1} = \frac{0}{- 1}$

Step 1.2.2

Divide $e^{\frac{1}{x}}$ by $1$ .

$e^{\frac{1}{x}} = \frac{0}{- 1}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $0$ by $- 1$ .

$e^{\frac{1}{x}} = 0$

Step 2

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

$\ln (e^{\frac{1}{x}}) = \ln (0)$

Step 3

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

Undefined

Step 4

There is no solution for $e^{\frac{1}{x}} = 0$

No solution