Calculus Examples

$v (6) = 58 (1 - e^{- 0.24 \cdot 6})$

Step 1

Simplify.

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Step 1.1

Multiply $- 0.24$ by $6$ .

$v (6) = 58 (1 - e^{- 1.44})$

Step 1.2

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

$v (6) = 58 (1 - \frac{1}{e^{1.44}})$

Step 1.3

Apply the distributive property.

$v (6) = 58 \cdot 1 + 58 (- \frac{1}{e^{1.44}})$

Step 1.4

Multiply $58$ by $1$ .

$v (6) = 58 + 58 (- \frac{1}{e^{1.44}})$

Step 1.5

Multiply $58 (- \frac{1}{e^{1.44}})$ .

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Step 1.5.1

Multiply $- 1$ by $58$ .

$v (6) = 58 - 58 \frac{1}{e^{1.44}}$

Step 1.5.2

Combine $- 58$ and $\frac{1}{e^{1.44}}$ .

$v (6) = 58 + \frac{- 58}{e^{1.44}}$

Step 1.6

Move the negative in front of the fraction.

$v (6) = 58 - \frac{58}{e^{1.44}}$

Step 2

Divide each term in $v (6) = 58 - \frac{58}{e^{1.44}}$ by $6$ and simplify.

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Step 2.1

Divide each term in $v (6) = 58 - \frac{58}{e^{1.44}}$ by $6$ .

$\frac{v (6)}{6} = \frac{58}{6} + \frac{- \frac{58}{e^{1.44}}}{6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{v \cdot 6}{6} = \frac{58}{6} + \frac{- \frac{58}{e^{1.44}}}{6}$

Step 2.2.1.2

Divide $v$ by $1$ .

$v = \frac{58}{6} + \frac{- \frac{58}{e^{1.44}}}{6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $58$ and $6$ .

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Step 2.3.1.1.1

Factor $2$ out of $58$ .

$v = \frac{2 (29)}{6} + \frac{- \frac{58}{e^{1.44}}}{6}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $2$ out of $6$ .

$v = \frac{2 \cdot 29}{2 \cdot 3} + \frac{- \frac{58}{e^{1.44}}}{6}$

Step 2.3.1.1.2.2

Cancel the common factor.

$v = \frac{2 \cdot 29}{2 \cdot 3} + \frac{- \frac{58}{e^{1.44}}}{6}$

Step 2.3.1.1.2.3

Rewrite the expression.

$v = \frac{29}{3} + \frac{- \frac{58}{e^{1.44}}}{6}$

Step 2.3.1.2

Multiply the numerator by the reciprocal of the denominator.

$v = \frac{29}{3} - \frac{58}{e^{1.44}} \cdot \frac{1}{6}$

Step 2.3.1.3

Cancel the common factor of $2$ .

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Step 2.3.1.3.1

Move the leading negative in $- \frac{58}{e^{1.44}}$ into the numerator.

$v = \frac{29}{3} + \frac{- 58}{e^{1.44}} \cdot \frac{1}{6}$

Step 2.3.1.3.2

Factor $2$ out of $- 58$ .

$v = \frac{29}{3} + \frac{2 (- 29)}{e^{1.44}} \cdot \frac{1}{6}$

Step 2.3.1.3.3

Factor $2$ out of $6$ .

$v = \frac{29}{3} + \frac{2 \cdot - 29}{e^{1.44}} \cdot \frac{1}{2 \cdot 3}$

Step 2.3.1.3.4

Cancel the common factor.

$v = \frac{29}{3} + \frac{2 \cdot - 29}{e^{1.44}} \cdot \frac{1}{2 \cdot 3}$

Step 2.3.1.3.5

Rewrite the expression.

$v = \frac{29}{3} + \frac{- 29}{e^{1.44}} \cdot \frac{1}{3}$

Step 2.3.1.4

Multiply $\frac{- 29}{e^{1.44}}$ by $\frac{1}{3}$ .

$v = \frac{29}{3} + \frac{- 29}{e^{1.44} \cdot 3}$

Step 2.3.1.5

Move $3$ to the left of $e^{1.44}$ .

$v = \frac{29}{3} + \frac{- 29}{3 \cdot e^{1.44}}$

Step 2.3.1.6

Move the negative in front of the fraction.

$v = \frac{29}{3} - \frac{29}{3 e^{1.44}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$v = \frac{29}{3} - \frac{29}{3 e^{1.44}}$

Decimal Form:

$v = 7.37636499 \dots$