| Rule name | Rule | Example |
|---|---|---|
| Product rule | ln(x ∙ y) = ln(x) + ln(y) | ln(3 ∙ 7) = ln(3) + ln(7) |
| Quotient rule | ln(x / y) = ln(x) - ln(y) | ln(3 / 7) = ln(3) - ln(7) |
| Power rule | ln(x y) = y ∙ ln(x) | ln(28) = 8∙ ln(2) |
| Ln derivative | f (x) = ln(x) ⇒ f ' (x) = 1 / x | |
| Ln integral | ∫ ln(x)dx = x ∙ (ln(x) - 1) + C | |
| Ln of negative number | ln(x) is undefined when x ≤ 0 | |
| Ln of zero | ln(0) is undefined | |
| Ln of one | ln(1) = 0 | |
| Ln of infinity | lim ln(x) = ∞ , |
when x→∞ | |
Derivative of natural logarithm (ln) function
The derivative of the natural logarithm function is the reciprocal function.
When
f (x) = ln(x)
The derivative of f(x) is:
f ' (x) = 1 / x
Integral of natural logarithm (ln) function
The integral of the natural logarithm function is given by:
When
f (x) = ln(x)
The integral of f(x) is:
∫ f (x)dx = ∫ ln(x)dx =
x ∙ (ln(x) - 1) + C