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If x^(m)y^(n)=(x+y)^(m+n), prove that : ...

If `x^(m)y^(n)=(x+y)^(m+n)`, prove that :
`(d^(2)y)/(dx^(2))=0`.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(k) (LONG ANSWER TYPE QUESTIONS (I))
  1. If y=(tan^(-1)x)^2, show that (x^2+1)^2y2+2x(x^2+1)y1=2

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  2. If y=(cot^(-1)x)^(2), then show that (x^(2)+1)^(2)(d^(2)y)/(dx^(2))+2x...

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  3. If y=(s in^(-1)\ x)/(sqrt(1-x^2)) , show that (1-x^2) (d^2\ y)/(dx^2)...

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

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  5. If y=log{x+sqrt(x^2+a^2)} , prove that: (x^2+a^2)(d^2y)/(dx^2)+x(dy)/(...

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  6. If y={x +sqrt(x^(2)+1)}^(m), then show that (x^(2)+1)(d^(2)y)/(dx^(2))...

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  7. If y=cos(mcos^(-1)x), then prove that : (1-x^(2))(d^(2)y)/(dx^(2))-x...

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  8. If y=sin(mtan^(-1)x), prove that : (1+x^(2))^(2)y(2)+2x(1+x^(2))y(1)...

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  9. If y=e^(msin^(-1)x),-1lexle1, show that : (1-x^(2))y(2)-xy(1)-m^(2)y...

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  10. If y=e^(acos^(-1)x),-1lexle1, show that : dy/dx=(-ae^(acos^(-1)x))/(sq...

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  11. If y=e^acos^((-1)x),-1lt=xlt=1,show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(d...

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  12. If y=e^(mtan^(-1)x), prove that : (1+x^(2))(d^(2)y)/(dx^(2))+(2x-m)d...

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  13. If y=e^(ax)cosbx, then prove that : (d^(2)y)/(dx^(2))-2ady/dx+(a^(2)...

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  14. If y=sin^(-1)x, show that (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx=0.

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  15. If y=tanx, then show that : (d^(2)y)/(dx^(2))=2ydy/dx

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

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  17. If x = f(t), y = g(t) possess second order derivatives for all t in (...

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  18. If y^(m)x^(n)=(x+y)^(m+n), then finddy/dx

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  19. If x^(m)y^(n)=(x+y)^(m+n), prove that : (d^(2)y)/(dx^(2))=0.

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  20. If p^(2)=a^(2)cos^(2)theta+b^(2)sin^(2)theta, then show that : p+(d^...

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