How do you find the second derivative of #ln |(x + 1)^2(x - 2)^4 / (2x + 9)|#?

1 Answer
Nov 27, 2016

Rewrite using properties of logarithms before differentiating.

Explanation:

We'll call the function #f#.

#f(x) = ln(((x+1)^2(x-2)^4)/(2x+9)) = 2ln(x+1)+4ln(x-2)-ln(2x+9)#

Use #d/dx(lnu) = 1/u (du)/dx#

#f'(x) = 2/(x+1)+4/(x-2)-2/(2x+9)#

Now use #d/dx(1/u) = -1/u^2 (du)/dx# to get

#f''(x) = -2/(x+1)^2 - 4/(x-2)^2 + 4/(2x+9)^2#