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Use logarithmic differentiation to find the derivatives of each of the functions in Exercises 49–58.

f(x)=lnxx

Short Answer

Expert verified

The derivative of function isy'=lnxx1lnx+ln(lnx)

Step by step solution

01

Step 1. Given Information

The given function isf(x)=lnxx

02

Step 2. Calculation    

First, we will take the log on both sides and then differentiate it,

lny=xlnlnx1yy'=x1lnx1x+ln(lnx)1yy'=1lnx+ln(lnx)y'=lnxx1lnx+ln(lnx)

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