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Find (d^2y)/(dx^2) when: tany=(sqrt(1+...

Find `(d^2y)/(dx^2)` when:
`tany=(sqrt(1+x^2)-1)/x`

Text Solution

Verified by Experts

The correct Answer is:
`-x/(x^2+1)^2`
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CHHAYA PUBLICATION-SECOND ORDER DERIVATIVE-Short Answer type Question
  1. Find f''(x) in each of the following cases: f(x)=e^xsin^2x

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  2. Find f''(x) in each of the following cases: f(x)=xsqrt(a^2-x^2)

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  3. Find (d^2y)/(dx^2) when: tany=(sqrt(1+x^2)-1)/x

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  4. Find (d^2y)/(dx^2) when: y=tan(x+y)

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  5. Find (d^2y)/(dx^2) when: sinx+cosy=1

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  6. Find (d^2y)/(dx^2) when: x^py^q=(x+y)^(p+q)

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  7. Findy2 in each of the following cases: x=acos^3theta,y=asin^3theta

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  8. Findy2 in each of the following cases: x=a(theta+sintheta),y=a(1-cost...

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  9. Findy2 in each of the following cases: x=a(t+1/t),y=a(t-1/t)

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  10. Findy2 in each of the following cases: x=e^t,y=sint at t=pi/2

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  11. Findy2 in each of the following cases: x=a(costheta+thetasintheta),y=...

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  12. Findy2 in each of the following cases: sinx=(2tantheta)/(1+tan^2theta...

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  13. Find y2 in each of the following cases: y=t^2+t^3,x=t-t^4

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  14. IF y^3=x^2+y^2, find (d^2y)/(dx^2) at y=1.

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  15. IF y=x/(x^2-x-2), find the value of y2 at x=1.

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  16. IF y=xsinx, prove that, x^2(d^2y)/(dx^2)-2xdy/dx+(2+x^2)y=0

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  17. If y=ae^(mx)+bcosmx, prove that, (d^2y)/(dx^2)+m^2y=2am^2e^(mx)

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  18. IF y=e^(-x)(cosx+sinx), show that ,y2+2y1+2y=0.

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  19. If y=e^x(sinx+cosx), then prove that, (d^2y)/(dx^2)-2dy/dx+2y=0

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  20. If y=x^3log""1/x, Prove that , xy2-2y1+3x^2=0.

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