Question

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!

Answer 1

Your "first-line" 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)

Answer 2

Thank you!