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Question
Find the derivative of the following function (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):
`(ax + b)/(px^2 + qx + r)`
Solution
`d/dx((ax + b)/(px^2 + qr + r)) = ([d/dx(ax + b)](px^2 + qx + r) - (ax + b) d/dx(px^2 + qx + r))/(px^2 + qx + r)^2`
= `(a.(px^2 + qx + r) - (ax + b). (2px +q))/(px^2 + qx + r)^2`
= `((apx^2 + aqx + ar) - [2apx^2 + (aq + 2bp)x + bq])/((px^2 + qx + r)^2)`
= `(-apx^2 + ar - 2bpx - bq)/((px^2 + qx + r)^2)`
= `(-apx^2 - 2bpx + ar - bq)/((px^2 + qx + r)^2)`
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