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): $(p x+q)\left(\frac{r}{x}+s\right)$
Let $f(x)=(p x+q)\left(\frac{r}{x}+s\right)$
By Leibnitz product rule,
$f^{\prime}(x)=(p x+q)\left(\frac{r}{x}+s\right)^{\prime}+\left(\frac{r}{x}+s\right)(p x+q)^{\prime}$
$=(p x+q)\left(r x^{-1}+s\right)^{\prime}+\left(\frac{r}{x}+s\right)(p)$
$=(p x+q)\left(-r x^{-2}\right)+\left(\frac{r}{x}+s\right) p$
$=(p x+q)\left(\frac{-r}{x^{2}}\right)+\left(\frac{r}{x}+s\right) p$
$=(p x+q)\left(\frac{-r}{x^{2}}\right)+\left(\frac{r}{x}+s\right) p$
$=\frac{-p r}{x}-\frac{q r}{x^{2}}+\frac{p r}{x}+p s$
$=p s-\frac{q r}{x^{2}}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.