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If y=(x+sqrt(1+x^2))^n then (1+x^2)(d^...

If `y=(x+sqrt(1+x^2))^n` then `(1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)`

A

`n^2y`

B

`n^2y`

C

`-y`

D

`2x^2y`

Text Solution

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The correct Answer is:
A
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TARGET PUBLICATION-DIFFERENTIATION -COMPETITIVE THINKING
  1. If x=at^2,y=2at, then (d^2x)/(dy^2)=

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  2. If x=f(t) and yy=g(t) are differentiable functions of t then (d^...

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  3. If y=(x+sqrt(1+x^2))^n then (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)

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  4. If x^2y^3=(x+y)^5, then (d^2y)/(dx^2) is

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  5. If x=sint and y=sinp t , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^...

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  6. If x=costheta, y=sin5theta then (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=

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  7. If y=e^sqrtx+e^(-sqrtx), then (x(d^2y)/(dx^2)+1/2.(dy)/(dx)) is equal ...

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  8. If x=2at^3,y=at^4, then (d^2y)/(dx^2) at t=2 is

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  9. If x=acostheta,y=bsintheta , then (d^2y)/(dx^2) when theta=pi/4 is gi...

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  10. If y = x^(3)log ( log (1+x) ) ,theny''(0) =

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  11. If x=e^t sin t , y=e^t cos t, t is a parameter , then (d^2y)/(dx^2) at...

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  12. If x=3 cos t and y=4 sin t, then (d^2y)/(dx^2) at the point (x0,y0)=(3...

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  13. If f:R in R is defined by f(x)=(x^(2)-ax+1)/(x^(2)+ax+1),0ltalt2, th...

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  14. If y=(a^(cos^-1x))/(1+a^(cos^-1x))andz=a^(cos^-1x),then (dy)/(dx)=

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  15. The first derivative of the function [cos^(-1)(sin sqrt((1+x)/2))+x^x]...

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  16. Let g(x) be the inverse of the function f(x), and f'(x)=1/(1+x^3) then...

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  17. Let f(x)=tan^-1 x. Then, f'(x)+f''(x) is = 0, when x is equal to

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  18. If x=a(t-(1)/(t)),y=a(t+(1)/(t)),"show that "(dy)/(dx)=(x)/(y)

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  19. If 2y=sin^-1(x+5y),then,(dy)/(dx) is equal to

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  20. Let f:R to R be a function such that f(x+y)=f(x)+f(y)"for all", x,y in...

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