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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 50 of 72
Marks: +1, -0
1ax2+bx+c\frac{1}{ax^2+bx+c}
Solution:  
Let f (x) = 1ax2+bx+c\frac{1}{ax^2+bx+c} ... (i)
Differentiating (i) with respect to x, we get
ddx\frac{d}{dx} (f (x)) =
(ax2+bx+c)⋅(1)′−1⋅(ax2+bx+c)′(ax2+bx+c)2\frac{(ax^2+bx+c)\cdot (1)' - 1\cdot (ax^2+bx+c)'}{(ax^2+bx+c)^2}
= (ax2+bx+c)(0)−(2ax+b)(ax2+bx+c)2\frac{(ax^2+bx+c)(0)-(2ax+b)}{(ax^2+bx+c)^2}
= −2ax−b(ax2+bx+c)2\frac{-2ax-b}{(ax^2+bx+c)^2}
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