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Find (dy)/(dx), when x=cos^(-1)1/(sqrt(1...

Find `(dy)/(dx),` when `x=cos^(-1)1/(sqrt(1+t^2))"and"y=sin^(-1)t/(sqrt(1+t^2)),tR`

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The correct Answer is:
1
Put `t=tan theta`
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RS AGGARWAL-DIFFERENTIATION-Exercise 10I
  1. Find (dy)/(dx), when x=(3a t)/(a+t^2)"and"y=(3a t^2)/(1+t^2)

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  2. Find (dy)/(dx) , when x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2)

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  3. Find (dy)/(dx), when x=cos^(-1)1/(sqrt(1+t^2))"and"y=sin^(-1)t/(sqrt(1...

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  4. "If "x=3cost-2cos^(3)t,y=3sint-2sin^(3)t," show that"(dy)/(dx)=cott.

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  5. if x=(1+lnt)/t^2 and y=(3+2lnt)/t then show that y(dy)/(dx)=2x((dy)/(d...

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  6. Find (dy)/(dx) , when x=a(1-costheta) and y=a(theta+sintheta) at theta...

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  7. If x=2costheta-cos2\ theta and y=2sintheta-sin2\ theta , prove that (d...

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  8. If x=sin^3t/(sqrtcos2t), y=cos^3t/sqrt(cos2t) show that dy/dx =0 at t=...

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  9. "If "x=(2costheta-cos 2theta)and y=(2sin theta-sin 2theta)," find "((d...

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  10. If x=a(theta-sintheta) , y=a(1+costheta) find (d^2y)/(dx^2)

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  11. Find the second derivative of : (i)x^(11)" "(ii)5^(x)" "(ii...

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  12. Find the second derivative of: (i)x sin x" "(ii)e^(2x)cos 3x" ...

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  13. If y=x+tanx , show that cos^2x\ (d^2y)/(dx^2)-2y+2x=0 .

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  14. If y=2sinx+3cosx ,show that (d^2y)/(dx^2)+y=0

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  15. If y=a cos (logx)+b sin (logx), prove that x^(2)y(2)+xy(1)+y=0.

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  16. If y=e^(-x)cosx, show that (d^(2)y)/(dx^(2))=2e^(-x)sinx.

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  17. If y=sec x-tanx,show that (cosx)(d^(2)y)/(dx^(2))=y^(2).

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  18. If y=("cosec "x+cotx), prove that (sinx)(d^(2)y)/(dx^(2))-y^(2)=0.

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  19. If y=tan^(-1)x , show that (1+x^2)(d^2y)/(dx^2)+2x(dy)/(dx)=0 .

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  20. If y=sin(sinx) then prove that (d^2y)/(dx^2)+tanx. (dy)/(dx)+y cos^2...

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