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Question

Mark the correct alternative in each of the following:

If y=1+1x21-1x2, then dydx=

(a) -4xx2-12 (b) -4xx2-1 (c) 1-x24x (d) 4xx2-1

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Solution


y=1+1x21-1x2 =x2+1x2-1

Differentiating both sides with respect to x, we get

dydx=x2-1×ddxx2+1-x2+1×ddxx2-1x2-12 Quotient rule =x2-1×2x+0-x2+1×2x-0x2-12 =2x3-2x-2x3-2xx2-12 =-4xx2-12

Hence, the correct answer is option (a).

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