# 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