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Chapter 2: Q 24 (page 238)

: Find the derivatives of the function

f(x)=xx

Short Answer

Expert verified

dydx=xxlogx+1

Step by step solution

01

Step 1:Given information

The given information isf(x)=xx

02

Step 2:Simplification

Given

f(x)=y=xx

Taking log both sides

logy=logxx

鈬�logy=xlogx (log property logab=bloga)

Differentiating w.r.t x

鈬�1ydydx=ddxxlogx

鈬�1ydydx=logx+x.1x (product rule of differentiation)

鈬�dydx=ylogx+1

鈬�dydx=xxlogx+1

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