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If y=ax^(n+1)+bx^(-n) then show that x^(...

If `y=ax^(n+1)+bx^(-n)` then show that `x^(2)y''=n(n+1)y`.

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SRISIRI PUBLICATION-DIFFERENTIATION-EXERCISE(SAQ)
  1. Find the derivative of xsinx from the first principle.

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  2. Find the derivative of cos^(2)x from the first principle.

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  3. Find the derivative of sqrt(x+1) from the first principle.

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  4. Using first principle, find the derivative of log(e)x where x in (0,oo...

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  5. Find the derivative of Tan^(-1)(secx+tanx).

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  6. Find the derivative of Tan^(-1)((3a^(2)x-x^(3))/(a(a^(2)-3x^(2)))).

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  7. Find the derivative of Tan^(-1)((sqrt(1+x^(2))-1)/(x)).

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  8. Differentiate Tan^(-1)(2x)/(1-x^(2)) w.r.t Sin^(-1)""(2x)/(1+x^(2)).

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  9. If y=ax^(n+1)+bx^(-n) then show that x^(2)y''=n(n+1)y.

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  10. If y=sin(sinx) then show that y''+(tanx)y'+ycos^(2)x=0.

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  11. Show that y=x+tanx satisfies the equation cos^(2)x(dy^(2))/(dx^(2))+2x...

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  12. If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y) then prove that dy/dx=(sqrt(1-y^...

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  13. If y=Tan^""(-1)((sqrt((1+x^(2)))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-...

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  14. If x^(logy)=logx then find dy/dx.

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  15. If x^(y)=y^(x) then show that dy/dx=(y(xlogy-y))/(x(ylogx-x)).

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  16. If y=xsqrt(a^(2)+x^(2))+a^(2)log(x+sqrt(a^(2)+x^(2))), then show that ...

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  17. Find the derivative of x^(tanx)+(sinx)^(cosx) w.r.to x.

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  18. if siny=xsin(a+y) then show that dy/dx=sin^(2)(a+y)/(sina).

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  19. If x=(3at)/(1+t^(3)),y=(3at^(2))/(1+t^(3)) then find dy/dx.

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  20. If x=a[(1-t^(2))/(1+t^(2))],y=(2bt)/(1+t^(2) then find dy/dx.

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