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Home  >>  CBSE XI  >>  Math  >>  Limits and Derivatives
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Find the derivative of the following functions ( it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers ) $\large\frac{ax+b}{px^2+qx+r}$

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Let $f(x) = \large\frac{ax+b}{px^2+qx+r}$
By qoutient rule,
$ f'(x) = \Large\frac{(px^2+qx+r) \large\frac{d}{dx}(ax+b)-(ax+b)\large\frac{d}{dx}(px^2+qx+r)}{(px^2+qx+r)^2}$
$ = \Large\frac{(px^2+qx+r)(a)-(ax+b)(2px+q)}{(px^2+qx+r)^2}$
$ = \Large\frac{apx^2+aqx+ar-2apx^2-aqx-2bpx-bq}{(px^2+qx+r)^2}$
$ = \Large\frac{-apx^2-2bpx+ar-bq}{(bx^2+qx+r)}$
answered Apr 12, 2014 by thanvigandhi_1
edited Apr 12, 2014 by thanvigandhi_1

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