數學二階導數問題

Q1.
y = 1/(x^2 - 9)
dy/dx = [-2x]/(x^2 - 9)^2
y" = [(x^2 - 9)^2(-2) - 2(-2x)(x^2 - 9)(2x)]/(x^2 - 9)^4.
= [(-2)(x^2 - 9) + 8x^2]/(x^2 - 9)^3
= (-2x^2 + 18 + 8x^2)/(x^2 - 9)^3
= (6x^2 + 18)/(x^2 - 9)^3.
= 6(x^2 + 3)/(x^2 - 9)^3.
Q2.
F(r) = y = 4^r
ln y = r ln4
1/y(y') = ln 4
y' = y ln4.............(1)
= ln4 (4^r).
From (1)
y" = ln4 y'
= (ln 4)^2 (4^r).