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Chapter 2: Q. 74 (page 223)

Use a direct application of the fact thatddxf-1x=1f'f-1xtoprovethatddxlnx=1x

Short Answer

Expert verified

The given differentiation has been proved.

Step by step solution

01

Step 1. Given Information 

The given function isf(x)=lnx

02

Step 2. Proof 

Since y=lnxandy=exare inverses, elnx=xfor all x in the domain 0,鈭�ofy=lnx.

By using property of inverse, we get,

elnx=xddxelnx=ddxxelnxddxlnx=1ddxlnx=1elnxddxlnx=1x

Hence, Proved.

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