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Question
(x + 1)2(x + 2)3(x + 3)4
Solution
Let y = (x + 1)2(x + 2)3(x + 3)4
∴ log y = `log [(x + 1)^2 * (x + 2)^3 (x + 3)^4]`
= `2log (x + 1) + 3 log (x + 2) + 4 log (x + 3)`
Differentiating w.r.t. x both sides, we get
`1/y * "dy"/"dx" = 2/(x + 1) + 3/(x + 2) + 4/(x + 3)`
∴ `"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))]`
= `(x + 1)^2 * (x + 2)^3 * (x + 3)^4 xx [(2(x + 3)(x + 3) + 3(x + 1)(x + 3) + 4(x + 1)(x + 2))/((x + 1)(x + 2)(x + 3))]`
= (x + 1)(x + 2)2(x + 3)3[9x2 + 34x + 29]
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