AP Calculus AB

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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 -

    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)

  • AP Calculus AB -

    Thank you!

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