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Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives2 Marks
Question
Differentiate the following functions.
$\frac{1}{\text{ax}^{2}+\text{bx}+\text{c}}$
✓

Answer

$\frac{\text{d}}{\text{dx}}\Big(\frac{1}{\text{ax}^{2}+\text{bx}+\text{c}}\Big)$
$=\frac{(\text{ax}^{2}+\text{bx}+\text{c})\frac{\text{d}}{\text{dx}}(1)-1\cdot\frac{\text{d}}{\text{dx}}(\text{ax}^{2}+\text{bx}+\text{c})}{(\text{ax}^{2}+\text{bx}+\text{c})^{2}}$
$=\frac{(\text{ax}^{2}+\text{bx}+\text{c})\times0-(2\text{ax}+\text{b})}{(\text{ax}^{2}+\text{bx}+\text{c})^{2}}$
$\frac{-(2\text{ax}+\text{b})}{(\text{ax}^{2}+\text{bx}+\text{c})^{2}}$
Hence, the required answer is $\frac{-(2\text{ax}+\text{b})}{(\text{ax}^{2}+\text{bx}+\text{c})^{2}}.$

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