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If y=tan^(-1)((a)/(x))+logsqrt((x-a)/(x+...

If `y=tan^(-1)((a)/(x))+logsqrt((x-a)/(x+a))`, then prove that `(dy)/(dx)=(2a^(3))/(x^(4)-a^(4))`.

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SHARAM PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXAMPLE
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  3. If y=tan^(-1)((a)/(x))+logsqrt((x-a)/(x+a)), then prove that (dy)/(dx)...

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  4. If (tan^(-1)x)^y + y^(cotx) =1then find (dy)/(dx).

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  5. If x^y = e^(x-y) then prove that (dy)/(dx)=logx/(1+logx)^2.

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  6. If y =x log (x/(a+bx))then prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^...

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  11. If x=acos^(3)theta,y=a sin^(3)theta,then find (d^2y)/dx^(2)

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  12. If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)

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  13. Find dy/dx if x^m y^n = (x/y)^(m+n)

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  14. Find (dy)/(dt), when y=sin^(-1)(2sqrt(t^(2)-1)/(t^(2)))

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  16. IF x^y=e^(x-y) then show that (dy)/(dx)=(logx)/[log(xe)]^2.

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  17. If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)

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  18. If x=a(cost+tsint) and y=a(sint-tcost), then find (d^(2)y)/(dx^(2)) at...

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  19. If cosx=sqrt(1/(1+t^2)),sin y=(2t)/(1+t^2) then show that (dy)/(dx) is...

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  20. Find (dy)/(dx), when y^(x)=x^(siny)

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