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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):
`(px+ q) (r/s + s)`
Solution
Let f(x) = `(px + q) (r/x + s)` ...(i)
Differentiating (i) with respect to x, we get
∴ `d/(dx) (f(x))` = `(px + q). (r/x + s) + (px + q) (r/x + s)`
= `(p + 0) (r/x + s) + (px + q). ((xr' - rx')/(x^2) + 0)`
= `p(r/x + s) + (px + q) ((0 - r)/x^2)`
= `p(r/x + s) - ((px + q)r)/x^2`
= `(pr)/x + ps - (pr)/x - (qr)/x^2`
= `ps - (qr)/x^2`
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