Differentiate `(x+1)^(2)(x+2)^(3)(x+3)^(4)` w.r.t. x.

1.	Differentiate `(x+1)^(2)(x+2)^(3)(x+3)^(4)` w.r.t. x.
Answer» Let `y=(x+1)^(2)(x+2)^(3)(x+3)^(4)." …(i)"` Taking logarithm on both sides of (i), we get `log y = 2log (x+1)+3log (x+2)+4 log (x+3)." …(ii)"` Differentiating both sides of (ii) w.r.t. x, we get `(1)/(y).(dy)/(dx)=(2)/((x+1))+(3)/((x+2))+(4)/((x+3))` `rArr(dy)/(dx)=y.[(2)/((x+1))+(3)/((x+2))+(4)/((x+3))]` `=(x+1)^(2)(x+2)^(3)(x+3)^(4).[(2)/((x+1))+(3)/((x+2))+(4)/((x+3))].`

Discussion

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