Calculus Examples

$f (0) = 8 e^{- x^{2}} x^{2} - 4 e^{- x^{2}}$

Step 1

Replace the variable $x$ with $0$ in the expression.

$f (0) = 8 e^{- {(0)}^{2}} {(0)}^{2} - 4 e^{- {(0)}^{2}}$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Raising $0$ to any positive power yields $0$ .

$f (0) = 8 e^{- 0} {(0)}^{2} - 4 e^{- {(0)}^{2}}$

Step 2.1.2

Multiply $- 1$ by $0$ .

$f (0) = 8 e^{0} {(0)}^{2} - 4 e^{- {(0)}^{2}}$

Step 2.1.3

Anything raised to $0$ is $1$ .

$f (0) = 8 \cdot (1 {(0)}^{2}) - 4 e^{- {(0)}^{2}}$

Step 2.1.4

Multiply $8$ by $1$ .

$f (0) = 8 {(0)}^{2} - 4 e^{- {(0)}^{2}}$

Step 2.1.5

Raising $0$ to any positive power yields $0$ .

$f (0) = 8 \cdot 0 - 4 e^{- {(0)}^{2}}$

Step 2.1.6

Multiply $8$ by $0$ .

$f (0) = 0 - 4 e^{- {(0)}^{2}}$

Step 2.1.7

Raising $0$ to any positive power yields $0$ .

$f (0) = 0 - 4 e^{- 0}$

Step 2.1.8

Multiply $- 1$ by $0$ .

$f (0) = 0 - 4 e^{0}$

Step 2.1.9

Anything raised to $0$ is $1$ .

$f (0) = 0 - 4 \cdot 1$

Step 2.1.10

Multiply $- 4$ by $1$ .

$f (0) = 0 - 4$

Step 2.2

Subtract $4$ from $0$ .

$f (0) = - 4$

Step 2.3

The final answer is $- 4$ .

$- 4$

Step 3