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DIFFERENTIATE FROM FIRST PRINCIPLES
(I)3X
(ii)X^2+2X+3
(iii)1/x^2

  • maths -

    I will do the middle one, you do others, looks like an assignment.

    f(x) = x^2 - 2x + 3

    dy/dx = LIM [ f(x+h) - f(x) ]/h as h---> 0

    f(x+h) = (x+h)^2 + 2(x+h) + 3
    = x^2 + 2xh + h^2 + 2x + 2h + 3

    Lim [ f(x+h) - f(x) ]/h
    = lim (x^2 + 2xh + h^2 + 2x + 2h + 3 - (x^2 + 2x + 3)/h
    = lim (2xh + h^2 + 2h)/h
    = lim 2x + h + 2
    = 2x + 2

    (each of the "lim" has h--> 2 under it)

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