Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Raise $\ln (3)$ to the power of $1$ .

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

Step 4

Raise $\ln (3)$ to the power of $1$ .

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

Step 5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 6

Add $1$ and $1$ .

$3^{x} \ln^{2} (3)$