ln[x^3(x+3)^2((x^2)+4))^7

Question

find the derivative

Answer 1

using the rules of logs, we can say
y = ln[x^3(x+3)^2((x^2)+4))^7}
= ln x^3 + ln(x+3)^2 + ln(x^2 + 4)^7
= 3lnx + 2ln(x+3) + 7ln(x^2+4)

dy/dx = 3/x + 2/(x+3) + 14x/(x^2+4)

simplify if needed