Calculus Examples

$y = 2 \cdot {(\frac{1}{3})}^{x}$

Step 1

Simplify $2 \cdot {(\frac{1}{3})}^{x}$ .

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Step 1.1

Simplify the expression.

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Step 1.1.1

Apply the product rule to $\frac{1}{3}$ .

$y = 2 \cdot \frac{1^{x}}{3^{x}}$

Step 1.1.2

One to any power is one.

$y = 2 \cdot \frac{1}{3^{x}}$

Step 1.2

Combine $2$ and $\frac{1}{3^{x}}$ .

$y = \frac{2}{3^{x}}$

Step 2

Graph the equation in order to determine the intervals over which it is increasing or decreasing.

Always Decreasing

Step 3