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If y=[x+sqrt(x^(2)-1)]^(15)+[x-sqrt(x^(2...

If `y=[x+sqrt(x^(2)-1)]^(15)+[x-sqrt(x^(2)-1)]^(15)` then `(x^(2)-1)(d^(2)y)/(dx^(2))+x""(dy)/(dx)` is equal to

A

125 y

B

`224y^(2)`

C

`225y^(2)`

D

`225y`

Text Solution

Verified by Experts

The correct Answer is:
D
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MCGROW HILL PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -Questions from Previous Years. AIEEE/JEE Main Papers
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  5. If y=[x+sqrt(x^(2)-1)]^(15)+[x-sqrt(x^(2)-1)]^(15) then (x^(2)-1)(d^(2...

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  6. If 2x=y^(1//5)+y^(-1//5) and (x^(2)-1)(d^(2)y)/(dx^(2))+lambdax""(dy)/...

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  7. If for x in (0,1//4), derivative of tan^(-1)((6xsqrt(x))/(1-9x^(3))) i...

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  9. If f(x)=|{:(cosx,x,1),(2sinx,x^(2),2x),(tan x,x,1):}|, then underset(x...

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  10. If f(x)=sin^(-1)((2xx3^(x))/(1+9^(x))), then f'(-(1)/(2)) is equal to

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  11. For each x in R, let f(x)=|x-1|,g(x)=cosx and phi(x) and f(g(2sinx))-g...

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  12. Let S={lambda, mu)epsilon R xxx R:f(t)=(|lambda|e^(|t|)-mu).sin(2|t|,)...

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  13. If x = 3 tan t and y = 3 sec t, then the value of (d^(2)y)/(dx^(2)) at...

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  14. Let f(x)={{:(max{|x|","x^(2)},,|x|lt 2),(8-2|x|,,2lt|x|le 4):} Let S...

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  15. Let f:(-1,1)toR be a function defined by max {-|x|,-sqrt(1-x^(2))}. If...

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  16. If x log(log x)-x^(2)+y^(2)=4(y gt 0), then (dy)/(dx) at x = e is equa...

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  18. Let f be a differentiable function such that f(1)=2 and f'(x)=f(x) for...

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  19. For x gt 1, if (2x)^(2y)=4e^(2x-2y), then (1+log 2x)^(2)(dy)/(dx) is e...

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