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(2^{8}) = 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→∞ 
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
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
Natural logarithm calculator ►