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if y=(1+1/x^(2))/(1-1/(x)^(2)),then (dy...

if `y=(1+1/x^(2))/(1-1/(x)^(2))`,then `(dy)/(dx)` is equal to

A

`(-4x)/(x^(2)-1)^(2)`

B

`(-4x)/(x^(2)-1)`

C

`(1-x^(2))/(4x)`

D

`(4x)/(x^(2)-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `y=(1+1/x^(2))/(1-1/x^(2)) rArr y=(x^(2)+1)/(x^(2)-1)`
`therefore (dy)/(dx) = ((x^(2)-1)2x-(x^(2)+1)(2x))/((x^(2)-1)^(2))` [by quotient rule]
`(dy)/(dx) = (2x(x^(2)-1-x^(2)-1))/(x^(2)-1)^(2)`
`=(2x(-2))/(x^(2)-1)^(2)=(-4x)/(x^(2)-1)^(2)`
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NCERT EXEMPLAR-LIMITS AND DERIVATIVES -OBJECTIVE TYPE QUESTIONS
  1. lim(xrarr1)(x^(m)-1)/(x^(n)-1) is equal to

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  2. lim(thetato0)(1-cos4theta)/(1-cos6theta) is equal to

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  3. lim(xrarr0)("cosec"x-cotx)/(x) is equal to

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  4. lim(xrarr0)(sinx)/(sqrt(x+1)-sqrt(1-x)) is equal to

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  5. lim(xrarr(pi//4))(sec^2x-2)/(tanx-1) is

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  6. lim(x->1)[(2x-3)(sqrtx-1)]/[2x^2+x-3]

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  7. If f(x) = { sin[x] /[x],[x] != 0 ; 0, [x] = 0} , Where[.] denotes the ...

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  8. lim(xrarr0)(|sinx|)/(x) is equal to

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  9. If f(x) ={x^2-1, 0 lt x lt 2 , 2x+3 , 2 le x lt 3then the quadratic eq...

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  10. lim(xrarr0)(tan2x-x)/(3x-sinx) is equal to

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  11. if f(x) =x-[x], in R, then f^(')(1/2) is equal to

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  12. if y=sqrt(x) + 1/sqrt(x), then (dy)/(dx) at x=1 is equal to

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  13. If f(x) =(x-4)/(2sqrt(x)), then f^(')(1) is equal to

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  14. if y=(1+1/x^(2))/(1-1/(x)^(2)),then (dy)/(dx) is equal to

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  15. if y=(sinx+cosx)/(sinx-cosx), then (dy)/(dx) at x=0 is equal to

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  16. if y=(sin(x+9))/(cosx), then (dy)/(dx) at x=0 is equal to

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  17. If f(x)=1+x+(x^2)/2++(x^(100))/(100), then f^(prime)(1) is equal to

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  18. Find the derivative of (x^(n)-a^(n))/(x-a) for some constant a.

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  19. If f(x)=x^(100)+x^(99)++x+1, then f^(prime)(1) is equal to

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  20. If f(x)=1-x^2-x^3+......-x^(99)+x^(100) then f^(prime)(1) equals

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