Calculus Examples

$f (1) = x e^{- x^{\frac{2}{32}}}$

Step 1

Replace the variable $x$ with $1$ in the expression.

$f (1) = (1) \cdot e^{- {(1)}^{\frac{2}{32}}}$

Step 2

Simplify the result.

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Step 2.1

Multiply $e^{- {(1)}^{\frac{2}{32}}}$ by $1$ .

$f (1) = e^{- {(1)}^{\frac{2}{32}}}$

Step 2.2

Cancel the common factor of $2$ and $32$ .

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Step 2.2.1

Factor $2$ out of $2$ .

$f (1) = e^{- 1^{\frac{2 (1)}{32}}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $32$ .

$f (1) = e^{- 1^{\frac{2 \cdot 1}{2 \cdot 16}}}$

Step 2.2.2.2

Cancel the common factor.

$f (1) = e^{- 1^{\frac{2 \cdot 1}{2 \cdot 16}}}$

Step 2.2.2.3

Rewrite the expression.

$f (1) = e^{- 1^{\frac{1}{16}}}$

Step 2.3

Simplify the expression.

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Step 2.3.1

One to any power is one.

$f (1) = e^{- 1 \cdot 1}$

Step 2.3.2

Multiply $- 1$ by $1$ .

$f (1) = e^{- 1}$

Step 2.4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$f (1) = \frac{1}{e}$

Step 2.5

The final answer is $\frac{1}{e}$ .

$\frac{1}{e}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{e}$

Decimal Form:

$0.36787944 \dots$

Step 4