Derivatives — MATHS STD 11 Science — Question

$\frac{\text{d}}{\text{dx}}\Big(\frac{\text{ax}+\text{b}}{\text{px}^2+\text{qx}+\text{r}}\Big)$

$=\frac{(\text{px}^2+\text{qx}+\text{r})\frac{\text{d}}{\text{dx}}(\text{ax}+\text{b})-(\text{ax}+\text{b})\frac{\text{d}}{\text{dx}}(\text{px}^2+\text{qx}+\text{r})}{(\text{px}^2+\text{qx}+\text{r})^2}$

$=\frac{(\text{px}^2+\text{qx}+\text{r})(\text{a})-(\text{ax}+\text{b})(\text{2xp}+\text{q})}{(\text{px}^2+\text{qx}+\text{r})^2}$

$=\frac{(\text{apx}^2+\text{aqx}+\text{ar})-(\text{2apx}^2+\text{aqx}+\text{2bpq}+\text{bq})}{(\text{px}^2+\text{qx}+\text{r})^2}$

$=\frac{-(\text{apx}^2+\text{2bpx}+\text{bq}-\text{ar})}{(\text{px}^2+\text{qx}+\text{r})^2}$