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Chapter 2: Q. 57 (page 222)

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

f(x)=lnxlnx

Short Answer

Expert verified

The derivative of function isy'=(lnx)lnx1x+ln(lnx)x

Step by step solution

01

Step 1. Given Information

The given function isf(x)=lnxlnx

02

Step 2. Calculation    

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

lny=lnlnxlnxlny=lnx路ln(lnx)1yy'=lnx1lnx1x+ln(lnx)1x1yy'=1x+ln(lnx)xy'=(lnx)lnx1x+ln(lnx)x

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