Calculate G′(−2) to 3 significant figures where G(x)=(−1x−2)^10(4x^2+4x+3)^12

Question

Please help me! I have no idea how to do this and it's due tonight

Answer 1

The derivative is not defined at x=-2...

Logrithmic differentiation:

y = (-1x-2)^120(4x^2+4x+3)

ln y = 120(4x^2+4x+3) ln (-1x-2)

y'/y = -120(4x^2+4x+3)/(-1x-2) + 120(8x+4) ln(-1x-2)

y' = -120(4x^2+4x+3)/(-1x-2) + 120(8x+4) ln(-1x-2) * y

FOr x=-2, the denomiantor is zero and the log of 0

is undefined

G(-2) is 0 which is not invertible and not loggable