Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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1 a X 2 + B X + C - Mathematics

\[\frac{1}{a x^2 + bx + c}\] 

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Solution

\[\frac{d}{dx}\left( \frac{1}{a x^2 + bx + c} \right)\]
\[ = \frac{d}{dx} \left( a x^2 + bx + c \right)^{- 1} \]
\[ = \left( - 1 \right) \left( a x^2 + bx + c \right)^{- 2} \frac{d}{dx}\left( a x^2 + bx + c \right) (\text{ Using the chain rule })\]
\[ = \left( - 1 \right) \left( a x^2 + bx + c \right)^{- 2} \left( 2ax + b \right)\]
\[ = \frac{- \left( 2ax + b \right)}{\left( a x^2 + bx + c \right)^2}\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Exercise 30.5 | Q 7 | Page 44
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