How to find the derivative of logarithmic functions?

Why is the general formula for the derivative of log x equal to 1/(x ln 10)? In this video, we will be discovering the derivative of logarithmic functions. First, by eliminating the common logarithm, we change the base of the logarithm to base e, which is natural logarithm. This is done to simplify the differentiation process. Then, the derivative can be found easily by using quotient rule, implicit differentiation, or just simple differentiation of ln x.
TIMECODES:
0:00 General Formula
0:22 Change of base
1:04 Finding the derivative