Posted by Jane on Sunday, September 18, 2011 at 1:56pm.
If y = (((3x^2)+ 5)^5)((x+2)^4),
then dy/dx = ?
I've gotten to the point where i have
(5((3x^2)+ 5)^4)(4(x+2)^3)(6x), what do i do next? It's a multiple choice question anf this is not one of the answers listed. Any help would be appreciated. Thanks!

AP Calculus AB  Reiny, Sunday, September 18, 2011 at 4:56pm
Your "firstline" derivative is
dy/dx = 5(3x^2 + 5)^4(6x)(x+2)^4 + 4(x+2)^3(3x^2+5)^5
= 2(x+2)^3(3x^2 + 5)^4 [ 15x(x+2) + 2(3x^2+5) ]
= 2(x+2)^3(3x^2 + 5)^4 [ 15x^2 + 30x + 6x^2 + 10 ]
= 2(x+2)^3(3x^2 + 5)^4 (21x^2 + 30x + 10) 
AP Calculus AB  Juliet, Thursday, November 10, 2011 at 10:32pm
Thank you!