Question:

\(\text{Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers)}\)\((px+q)(\frac{r}{x}+s).\)

Updated On: Oct 23, 2023
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Solution and Explanation

\(\text{Let }, f(x)=(px+q)(\frac{r}{x}+s)\)

\(\text{By Leibnitz product rule,}\)

\(=f'(x)=(px+q)(\frac{r}{x}+s)'+(\frac{r}{x}+s)(px+q)'\)

\(=(px+q)(rx^{-1}+s)'+(\frac{r}{s})(p)\)

\(=(px+q)(-rx^{-2})+(\frac{r}{s}+s)p\)

\(=(px+q)(\frac{-r}{x^2})+(\frac{r}{s})p\)

\(=-\frac{pr}{x}-\frac{qr}{x^2}+\frac{pr}{x}+ps\)

\(=ps-\frac{qr}{x^2}\)

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Concepts Used:

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