Derivative of logarithm

1. (loga x)' = 1/(x ln a) 
   The derivative of the logarithm with base a of the variable x is equal to one divided by the product of the variable and the natural logarithm of a.
2. (loga f(x))' = f '(x) / (f(x) ln a) 
   The derivative of the logarithm with the base a of the function f(x) is equal to the fraction whose numerator contains the derivative of the function f(x),
   and whose denominator contains the product of f(x) and the natural logarithm of a
3. (ln x)' = 1/x 
   The derivative of the natural logarithm is 1/х 
4. The double derivative of the natural logarithm x is equal to minus one divided by the square of x
5. (ln f(x) )' = f '(x) / f(x) 
   The derivative of the natural logarithm of the function f(x) is equal to the fraction whose numerator contains the derivative of this function, 
   and whose denominator contains the function itself