What the derivative of lnx?

2 Answers
Mar 20, 2018

#1/x#

Explanation:

#y=lnx#

by definition of logarithms

#x=e^y#

differentiate #wrty#

#(dx)/(dy)=e^y#

but

#(dy)/(dx)=1/((dx)/(dy))#

#:.(dy)/(dx)=1/e^y#

#=>(dy)/(dx)=1/x#

Mar 20, 2018

#1/x#

Explanation:

By definition, #ln k=int_1^k1/x\ dx# so the derivative is the original #1/x#, because the integral is the "anti-derivative" and vice versa.