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 $- 1$ by ${(- 1)}^{\frac{2}{32}}$ by adding the exponents.

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Step 2.1.1

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

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Step 2.1.1.1

Raise $- 1$ to the power of $1$ .

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

Step 2.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.1.2

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

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Step 2.1.2.1

Factor $2$ out of $2$ .

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

Step 2.1.2.2

Cancel the common factors.

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Step 2.1.2.2.1

Factor $2$ out of $32$ .

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

Step 2.1.2.2.2

Cancel the common factor.

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

Step 2.1.2.2.3

Rewrite the expression.

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

Step 2.1.3

Write $1$ as a fraction with a common denominator.

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

Step 2.1.4

Combine the numerators over the common denominator.

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

Step 2.1.5

Add $16$ and $1$ .

$f (- 1) = - 1 \cdot e^{{(- 1)}^{\frac{17}{16}}}$

Step 2.2

Rewrite $- 1 e^{{(- 1)}^{\frac{17}{16}}}$ as $- e^{{(- 1)}^{\frac{17}{16}}}$ .

$f (- 1) = - e^{{(- 1)}^{\frac{17}{16}}}$

Step 2.3

The final answer is $- e^{{(- 1)}^{\frac{17}{16}}}$ .

$- e^{{(- 1)}^{\frac{17}{16}}}$

Step 3