Q. 365.0( 2 Votes )

Differentiate each of the following w.r.t. x

(x + 1)2 (x + 2)3 (x + 3)4

Answer :

We have given, (x + 1)2 (x + 2)3 (x + 3)4

Let Assume, y=(x + 1)2 (x + 2)3 (x + 3)4


So,


y=(x + 1)2 (x + 2)3 (x + 3)4


Taking log both side


Log y=log [(x + 1)2 (x + 2)3 (x + 3)4]


Log y=log(x + 1)2 +log(x + 2)3 +log(x + 3)4]


Log y=2log(x + 1) +3log(x + 2) +4log(x + 3)]


Differentiate w.r.t x






= (x+1)(x+2)2(x+3)3[9x2+34x+29]


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