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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)/(cx + d)`
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Solution
Let f(x) = `(ax + b)/(cx + d)`
∴ f'(x) = `([d/dx (ax + b)](cx + d) - (ax + b) d/dx (cx + d))/((cx + d)^2)`
= `(a(cx + d) - (ax + b) .c)/((cx + d)^2)`
= `(acx + ad - acx - bc)/((cx + d)^2)`
= `(ad - bc)/((cx + d)^2)`
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