Calculus Examples

$v (10) = 100 e^{- 0.1 t} + 0.1 t$

Step 1

Divide each term in $v (10) = 100 e^{- 0.1 t} + 0.1 t$ by $10$ .

$\frac{v \cdot 10}{10} = \frac{100 e^{- 0.1 t}}{10} + \frac{0.1 t}{10}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $10$ .

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Step 2.1.1

Cancel the common factor.

$\frac{v \cdot 10}{10} = \frac{100 e^{- 0.1 t}}{10} + \frac{0.1 t}{10}$

Step 2.1.2

Divide $v$ by $1$ .

$v = \frac{100 e^{- 0.1 t}}{10} + \frac{0.1 t}{10}$

Step 3

Simplify the right side.

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Step 3.1

Simplify each term.

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Step 3.1.1

Cancel the common factor of $100$ and $10$ .

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Step 3.1.1.1

Factor $10$ out of $100 e^{- 0.1 t}$ .

$v = \frac{10 (10 e^{- 0.1 t})}{10} + \frac{0.1 t}{10}$

Step 3.1.1.2

Cancel the common factors.

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Step 3.1.1.2.1

Factor $10$ out of $10$ .

$v = \frac{10 (10 e^{- 0.1 t})}{10 (1)} + \frac{0.1 t}{10}$

Step 3.1.1.2.2

Cancel the common factor.

$v = \frac{10 (10 e^{- 0.1 t})}{10 \cdot 1} + \frac{0.1 t}{10}$

Step 3.1.1.2.3

Rewrite the expression.

$v = \frac{10 e^{- 0.1 t}}{1} + \frac{0.1 t}{10}$

Step 3.1.1.2.4

Divide $10 e^{- 0.1 t}$ by $1$ .

$v = 10 e^{- 0.1 t} + \frac{0.1 t}{10}$

Step 3.1.2

Factor $0.1$ out of $0.1 t$ .

$v = 10 e^{- 0.1 t} + \frac{0.1 (t)}{10}$

Step 3.1.3

Factor $10$ out of $10$ .

$v = 10 e^{- 0.1 t} + \frac{0.1 (t)}{10 (1)}$

Step 3.1.4

Separate fractions.

$v = 10 e^{- 0.1 t} + \frac{0.1}{10} \cdot \frac{t}{1}$

Step 3.1.5

Divide $0.1$ by $10$ .

$v = 10 e^{- 0.1 t} + 0.01 \frac{t}{1}$

Step 3.1.6

Cancel the common factor of $0.01$ .

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Step 3.1.6.1

Factor $0.01$ out of $1$ .

$v = 10 e^{- 0.1 t} + 0.01 \frac{t}{0.01 \cdot 100}$

Step 3.1.6.2

Cancel the common factor.

$v = 10 e^{- 0.1 t} + 0.01 \frac{t}{0.01 \cdot 100}$

Step 3.1.6.3

Rewrite the expression.

$v = 10 e^{- 0.1 t} + \frac{t}{100}$