What is the derivative of y = ln[(x+1)^4 (x+7)^2 (x+2)^3]

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We have to find the derivative of y = ln[(x+1)^4*(x+7)^2*(x+2)^3]

First simplify the expression using the properties of logarithms: log(a*b) = log a  + log b and log(a^b) = b*log a

y = ln[(x+1)^4*(x+7)^2*(x+2)^3]

=> y = ln(x+1)^4 + ln(x+7)^2 + ln(x+2)^3

=> y = 4*ln(x+1) + 2*ln(x+7) + 3*ln(x+2)

Now we differentiate the function

y' = 4/(x + 1) + 2 /(x + 7) + 3/(x + 2)

The derivative of the given function is 4/(x + 1) + 2 /(x + 7) + 3/(x + 2)

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