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# Solution for If Y = 1 1 + X a − B + C − B + 1 1 + X B − C + X a − C + 1 1 + X B − a + X C − a Then D Y D X is Equal to - CBSE (Science) Class 12 - Mathematics

ConceptSimple Problems on Applications of Derivatives

#### Question

If $y = \frac{1}{1 + x^{a - b} +^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} + \frac{1}{1 + x^{b - a} + x^{c - a}}$ then $\frac{dy}{dx}$  is equal to

(a) 1
(b) $\left( a + b + c \right)^{x^{a + b + c - 1}}$
(c) 0
(d) none of these

#### Solution

(c) 0

$\text { We have },$
$y = \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} + \frac{1}{1 + x^{b - a} + x^{c - a}}$
$= \frac{1}{1 + \frac{x^a}{x^b} + \frac{x^c}{x^b}} + \frac{1}{1 + \frac{x^b}{x^c} + \frac{x^a}{x^c}} + \frac{1}{1 + \frac{x^b}{x^a} + \frac{x^c}{x^a}}$
$= \frac{x^b}{x^b + x^a + x^c} + \frac{x^c}{x^c + x^b + x^a} + \frac{x^a}{x^a + x^b + x^c}$
$= \frac{x^b}{x^a + x^b + x^c} + \frac{x^c}{x^a + x^b + x^c} + \frac{x^a}{x^a + x^b + x^c}$
$= \frac{x^b + x^c + x^a}{x^a + x^b + x^c}$
$= \frac{x^a + x^b + x^c}{x^a + x^b + x^c}$
$= 1$
$\therefore \frac{dy}{dx} = \frac{d}{dx}\left( 1 \right) = 0$

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Solution If Y = 1 1 + X a − B + C − B + 1 1 + X B − C + X a − C + 1 1 + X B − a + X C − a Then D Y D X is Equal to Concept: Simple Problems on Applications of Derivatives.
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