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COLLEGE CALCULUS. HELP!

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Let f(x)=(-3x^2+6)^4(9x^2+7)^14, Find f'(x).

f'(x)= (-3^2+6)^4 d/dx(9x^2+7)^14+(9x^2+7) d/dx(-3x^2+6)^4
=(-3x^2+6)x14(9x^2+7)^13 d/dx(9x^2+7)+(9x^2+7)^14x4(-3x^2+6)^3 d/dx(-3x^2+6)
=14(-3x+6)^4(9x^+7)^13 (18x)+ 4(9x^2+7)(-3x^2+6)^3 (-6x)

  • COLLEGE CALCULUS. HELP! - ,

    i got stuck

  • COLLEGE CALCULUS. HELP! - ,

    Start with the product rule, and take it slowly.

    (d/dx)[(-3x^2+6)^4(9x^2+7)^14]
    =(d/dx)[(-3x^2+6)^4](9x^2+7)^14 + (-3x^2+6)^4 (d/dx)[(9x^2+7)^14]
    =4(-3x^2+6)^3 (d/dx)[-3x^2+6](9x^2+7)^14 + (-3x^2+6)^4*14(9x^2+7)^13(d/dx)[9x^2+7)
    =4(-3x^2+6)^3 (-6x) + (-3x^2+6)^4*14(9x^2+7)^13 (18x)
    Now take out the common factors (-3x^2+6)^3(9x^2+7)^13 to get

    =(-3x^2+6)^3(9x^2+7)^13[4(-6x)(9x^2+7) + (-3x^2+6)14(18x)]
    =(-3x^2+6)^3(9x^2+7)^13[-216x^3+168x + -756x^3+1512x]
    =(-3x^2+6)^3(9x^2+7)^13[-972x^3+1344x]
    =(-3x^2+6)^3(9x^2+7)^13(-12x)(81x^2-112)
    =324x(x^2-2)^3(9x^2+7)^13(81x^2-112)

  • COLLEGE CALCULUS. HELP! - ,

    hey how u get 324x?

  • COLLEGE CALCULUS. HELP! - ,

    (-3x^2+6)^3(9x^2+7)^13(-12x)(81x^2-112)
    =3^3(-12x)(-2+x^2)^3(9x^2+7)^13(81x^2-112)
    =27*12x(x^2-2)^3(9x^2+7)^13(81x^2-112)
    =324x(x^2-2)^3(9x^2+7)^13(81x^2-112)

  • COLLEGE CALCULUS. HELP! - ,

    i got it thanks

  • COLLEGE CALCULUS. HELP! - ,

    You're welcome! :)

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