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If x=int(0)^(y)(1)/(sqrt(1+4t^(2))) dt, ...

If `x=int_(0)^(y)(1)/(sqrt(1+4t^(2)))` dt, then `(d^(2)y)/(dx^(2))`, is

A

2y

B

4y

C

8y

D

6y

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The correct Answer is:
B
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OBJECTIVE RD SHARMA-DIFFERENTIATION-Exercise
  1. If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (-2)/(1+x^2) for all ...

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  2. If x=int(0)^(y)(1)/(sqrt(1+4t^(2))) dt, then (d^(2)y)/(dx^(2)), is

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  3. If f(x)=sqrt(x^(2)-2x+1), then f' (x) ?

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  4. If f(x)=sqrt(1-sin2x), then f'(x) equals

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  5. If f(x)=|x^2-5x+6|,t h e nf^(prime)(x)e q u a l s 2x-5for2<x<3 5-2xf...

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  6. If x^(2)+y^(2)=a^(2)" and "k=1//a then k is equal to

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  7. If f(x)=sinx" and "g(x)=sgn sinx, then g'(1) equals

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  8. If y=sin^(-1)(x/2)+cos^(-1)(x/2) then (dy)/(dx)=

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  9. If y=cos^(-1)((2cosx-3sinx)/(sqrt(13))), then (dy)/(dx), is

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  10. If y=x+e^x , then (d^2x)/(dy^2) is equal to

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  11. If F(x)=(1)/(x^(2))int(4)^(x)(4t^(2)-2F'(t)) dt, then F'(4) equals

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  12. If y^2 = P(x) is polynomial of degree 3, then 2(d/dx)(y^3.d^2y/dx^2) i...

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  13. if 2^x+2^y=2^(x+y) then the value of (dy)/(dx) at x=y=1

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  14. The derivative of tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)...

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  15. If y=tan^(-1){((log)e(e//x^2))/((log)e(e x^2))}+tan^(-1)((3+2\ (log)e ...

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  16. The expression of (dy)/(dx) of the function y=a^(x^(a^(x...^(oo)))), i...

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  17. If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y), then (dy)/(dx) equals

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  18. If y=e^(1+log(e)x), then the value of (dy)/(dx) is equal to

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  19. If x^(y)=e^(x-y), then (dy)/(dx) is equal to

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  20. Let f(x)=(x^(2))/(1-x^(2)),xne0,+-1, then derivative of f(x) with resp...

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