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differentiate with respect to x,
y = (x+1)2/(x+2)3(x+3)4

Let y = x+12x+23 x+34⇒log y = log x+12x+23 x+34⇒log y = log x+12 - log x+23 x+34⇒log y = log x+12 - log x+23 - log x+34⇒log y = 2 log x+1 - 3 log x+2 - 4 log x+3Differentiating both sides with respect to x, we get1ydydx = 2x+1 - 3x+2 - 4x+3⇒dydx = y2x+1 - 3x+2 - 4x+3⇒dydx = x+12x+23 x+342x+1 - 3x+2 - 4x+3

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