Find the Derivative - d/dx 7.4 natural log of x+3

$7.4 \ln (x) + 3$

By the Sum Rule, the derivative of $7.4 \ln (x) + 3$ with respect to $x$ is $\frac{d}{d x} [7.4 \ln (x)] + \frac{d}{d x} [3]$ .

$\frac{d}{d x} [7.4 \ln (x)] + \frac{d}{d x} [3]$

Evaluate $\frac{d}{d x} [7.4 \ln (x)]$ .

Since $7.4$ is constant with respect to $x$ , the derivative of $7.4 \ln (x)$ with respect to $x$ is $7.4 \frac{d}{d x} [\ln (x)]$ .

$7.4 \frac{d}{d x} [\ln (x)] + \frac{d}{d x} [3]$

The derivative of $\ln (x)$ with respect to $x$ is $\frac{1}{x}$ .

$7.4 \frac{1}{x} + \frac{d}{d x} [3]$

Combine $7.4$ and $\frac{1}{x}$ .

$\frac{7.4}{x} + \frac{d}{d x} [3]$

Differentiate using the Constant Rule.

Since $3$ is constant with respect to $x$ , the derivative of $3$ with respect to $x$ is $0$ .

$\frac{7.4}{x} + 0$

Add $\frac{7.4}{x}$ and $0$ .

$\frac{7.4}{x}$