Calculus Examples

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

Step 1

Since $\frac{1}{\ln (3)}$ is constant with respect to $x$ , the derivative of $\frac{3^{x}}{\ln (3)}$ with respect to $x$ is $\frac{1}{\ln (3)} \frac{d}{d x} [3^{x}]$ .

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

Step 2

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

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

Step 3

Simplify terms.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Cancel the common factor of $\ln (3)$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Divide $3^{x}$ by $1$ .

$3^{x}$