Calculus Examples

$f (x) = \ln (x) + 1$

Step 1

By the Sum Rule, the derivative of $\ln (x) + 1$ with respect to $x$ is $\frac{d}{d x} [\ln (x)] + \frac{d}{d x} [1]$ .

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

Step 2

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

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

Step 3

Differentiate using the Constant Rule.

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Step 3.1

Since $1$ is constant with respect to $x$ , the derivative of $1$ with respect to $x$ is $0$ .

$\frac{1}{x} + 0$

Step 3.2

Add $\frac{1}{x}$ and $0$ .

$\frac{1}{x}$