1.函数y=(2+x^3)^2的导数为( )

1个回答

  • 1.复合求导

    lny=2(2+x^3)^(2-1)*(2+x^3)'

    =2(2+x^3)*3x^(3-1)

    =6x^2(2+x^3)

    2.也是复合求导

    =8(1+2x^2)^(8-1)*(1+2x^2)'

    =8(1+2x^2)^7*2*2x^(2-1)

    =8(1+2x^2)^7*2*2x^(2-1)

    =32x(1+2x^2)^7

    3.y'=(x-1)'*(x-2)(x-3)...(x-100)+(x-2)'*(x-1)(x-3)...(x-100)+.+(x-100)'*(x-1)(x-2)...(x-99)

    =(x-2)(x-3)...(x-100)+(x-1)(x-3)...(x-100)+(x-1)(x-2)(x-4)...(x-100)+(x-1)(x-2)...(x-99)

    =[1/(x-1)+1/(x-2)+…+1/(x-100)](x-1)(x-2)…(x-100)