How do you find the derivative of #log_(3)x#?
1 Answer
Mar 15, 2016
Explanation:
There is an identity that states
#log_a(b) = frac{ln(a)}{ln(b)}# ,
for
So, we can write
#log_3(x) = ln(x)/ln(3)#
for
So to find the derivative, it helps if you know that
#frac{"d"}{"d"x}(ln(x)) = 1/x# .
So,
#frac{"d"}{"d"x}(log_3(x)) = frac{"d"}{"d"x}(ln(x)/ln(3))#
#= 1/ln(3) frac{"d"}{"d"x}(ln(x))#
#= 1/(xln(3))# .