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Find the derivative of 2x+3/ 3x-2
using first principle method.

  • maths -

    you meant:
    f(x) = y = (2x+3)/(3x-2)

    so f(x+h) = (2x + 2h + 3)/(3x + 3h - 2)

    dy/dx = lim [ (2x+2h+3)/(3x+3h-2) - (2x+3)/(3x-2) ]/h , as h --->0
    = lim [ ((2x + 2h + 3)(3x-2) - (2x+3)(3x+3h+2))/((3x+3h-2)(3x+h))]/h
    = lim [ (5h/((3x+3h-2)(3x-2))]/h , as h -->0
    = lim 5/((3x+3h-2)(3x-2)) , as h -->0
    = 5/(3x-2)^2

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