Example 12 __
If y = (x + 1)ln^2 (x + 1), find .
SOLUTION: (Product and Chain Rules)
= 2 ln (x + 1) + ln^2 (x + 1).
Example 13 __
If g(x) = ( 1 + sin^2 3 x )^4 , find g′( ).
SOLUTION: g′(x) = 4( 1 + sin^2 3 x )^3 (2 sin 3x cos 3x) · (3)
= 24( 1 + sin^2 3 x )^3 (sin 3x cos 3x).
Then g′( )=24(1 + (−1)^2 )^3 (− 1 · 0) = 24 · 8 · 0 = 0.
Example 14 __
If , find y′.
SOLUTION:
Example 15 __
If
SOLUTION: u = ln ( v^2 + 2 v − 1 ) so