Barrons AP Calculus

(Marvins-Underground-K-12) #1
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

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