What is the derivative of #y=log_10(x)#?
1 Answer
The answer is
#y'=log_10(e)*1/x#
Solution
Suppose we have
#log_a(b)=log_a(e)*log_e(b)#
Similarly, function
#y=log_10(e)*log_e(x)#
Let's say we have,
then,
Now, this is quite straightforward to differentiate, as
Hence:
#y'=log_10(e)*1/x#
Alternate solution:
Another common approach is to use the change of base formula, which says that:
#log_a(b) =ln(b)/ln(a)#
From change of base we have
This we can differentiate as long as we remember that
#1/ln(10)# is just a constant multipler.
Doing the problem this way gives a result of