Q. 54.2( 71 Votes )

Differentiate the functions given in w.r.t. x.

(x + 3)2. (x + 4)3. (x + 5)4

Answer :

Given: (x + 3)2. (x + 4)3. (x + 5)4

Let y= (x + 3)2. (x + 4)3. (x + 5)4


Taking log on both sides, we get


log y = log((x + 3)2. (x + 4)3. (x + 5)4)


log y = log(x + 3)2 + log(x + 4)3 + log(x + 5)4


log y = 2.log(x + 3) + 3.log(x + 4) + 4.log(x + 5)4


Now, differentiate both sides with respect to x







= (x + 3)(x + 4)2(x + 5)3(9x2 + 70x + 133)

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