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Question

Differentiate the following functions with respect to x :

x2x+1x2+x+1


Solution

We have,

ddx(x2x+1x2+x+1)

Using quotient rule,

(x2+x+1)ddx(x2x+1)(x2x1)ddx(x2+x+1)(x2+x+1)2

=(x2+x+1)(2x1)(x2x+1)(2x+1)(x2+x+1)

=(x2+1x)(2x1)(x2x+1)(2x+1)(x2+x+1)2

=2x3+2x+2x2x21x2x3+2x22xx2+x1(x2+x+1)2

=2x22(x2+x+1)2=2(x21)(x2+x+1)2


Mathematics
RD Sharma
Standard XI

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