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If y =x log (x/(a+bx))then prove that x^...

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

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SHARAM PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXAMPLE
  1. If (tan^(-1)x)^y + y^(cotx) =1then find (dy)/(dx).

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

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

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  4. If y=(sinx)^(x)+sin^(-1)sqrt(x), then find (dy)/(dx).

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  5. If x=2cos theta-cos 2theta and y=2sin theta-sin 2 theta, then prove th...

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  6. Differentiate the following function w.r.t. x, (logx)^(x)+x^(logx).

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  7. If y=log[x+sqrt(x^(2)+1)], then prove that (x^(2)+1)(d^(2)y)/(dx^(2))+...

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

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

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

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

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  12. If x=asec theta, y=b tan theta, then prove that (d^(2)y)/(dx^(2))=-(b^...

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

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

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

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

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

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  18. If y^2 cot x = x^2 cot y then find (dy)/(dx).

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  19. Find the derivative of x^(sinx) w.r.t.x.

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  20. Differentiate sin^(-1) ((2X)/(1+X^(2))) with respect to cos^(-1) ((1-X...

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