Question
Differentiate the following functions.
$(\text{ax}^{2}+\cot\text{x})(\text{p}+\text{q}\cos\text{x})$
$(\text{ax}^{2}+\cot\text{x})(\text{p}+\text{q}\cos\text{x})$
✓
Answer
$\frac{\text{d}}{\text{dx}}(\text{ax}^{2}+\cot\text{x})(\text{p}+\text{q}\cos\text{x})$
$=(\text{ax}^{2}+\cot\text{x})\frac{\text{d}}{\text{dx}}(\text{p}+\text{q}\cot\text{x})+(\text{p}+\text{q}\cos\text{x})\frac{\text{d}}{\text{dx}}(\text{ax}^{2}+\cot\text{x})$
$=(\text{ax}^{2}+\cot\text{x})(-\text{q}\sin\text{x})+(\text{p}\sin\text{x})+(\text{p}+\text{q}\cos\text{x})(2\text{ax}-\text{cosec}^{2}\text{x}\big)$
Hence, the required answer is
$(\text{ax}^{2}+\cot\text{x})(-\text{q}\sin\text{x})+(\text{p}\sin\text{x})+(\text{p}+\text{q}\cos\text{x})(2\text{ax}-\text{cosec}^{2}\text{x}\big)$
$=(\text{ax}^{2}+\cot\text{x})\frac{\text{d}}{\text{dx}}(\text{p}+\text{q}\cot\text{x})+(\text{p}+\text{q}\cos\text{x})\frac{\text{d}}{\text{dx}}(\text{ax}^{2}+\cot\text{x})$
$=(\text{ax}^{2}+\cot\text{x})(-\text{q}\sin\text{x})+(\text{p}\sin\text{x})+(\text{p}+\text{q}\cos\text{x})(2\text{ax}-\text{cosec}^{2}\text{x}\big)$
Hence, the required answer is
$(\text{ax}^{2}+\cot\text{x})(-\text{q}\sin\text{x})+(\text{p}\sin\text{x})+(\text{p}+\text{q}\cos\text{x})(2\text{ax}-\text{cosec}^{2}\text{x}\big)$
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