Calculus Examples

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

Step 1

Differentiate using the Exponential Rule which states that $\frac{d}{d x} [a^{x}]$ is $a^{x} \ln (a)$ where $a$ = $\frac{1}{3}$ .

${(\frac{1}{3})}^{x} \ln (\frac{1}{3})$

Step 2

Simplify.

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Step 2.1

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

$\frac{1^{x}}{3^{x}} \ln (\frac{1}{3})$

Step 2.2

Combine terms.

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Step 2.2.1

One to any power is one.

$\frac{1}{3^{x}} \ln (\frac{1}{3})$

Step 2.2.2

Combine $\frac{1}{3^{x}}$ and $\ln (\frac{1}{3})$ .

$\frac{\ln (\frac{1}{3})}{3^{x}}$