Asked by Kevin

F(x)= ln((3x+6)^4 (x^3 -2)^5 )

F'(x)=
Answered by Reiny
I would first simplify that log expression

= log (3x+6)^4 + log (x^3-2)^5
= 4 log (3x+6) + 5 log (x^3 - 2)
now take the derivative

f ' (x) = 4(3/(3x+6) + 5(3x2)/(x^3 - 2)
= 4/(x+2) + 15x^2/(x^3 - 2)

add them up if needed.

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