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Derivatives — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSDerivatives5 Marks
Question
Differentiate the following functions with respect to x:

$\frac{1}{\text{ax}^2+\text{bx}+\text{c}}$

✓

Answer

We have,

$\frac{\text{d}}{\text{dx}}\Big(\frac{1}{\text{ax}^2+\text{bx}+\text{c}}\Big)$

$=\frac{(\text{ax}^2+\text{bx}+\text{c})\frac{\text{d}}{\text{dx}}(1)-(1)\frac{\text{d}}{\text{dx}}(\text{ax}^2+\text{bx}+\text{c})}{(\text{ax}^2+\text{bx}+\text{c})^2}$

$=\frac{(\text{ax}^2+\text{bx}+\text{c})(0)-(1)(\text{2ax}+\text{b})}{(\text{ax}^2+\text{bx}+\text{c})^2}$

$=\frac{-(\text{2ax}+\text{b})}{(\text{ax}^2+\text{bx}+\text{c})^2}$

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