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Using mathematical induction prove that : `d/(dx)(x^n)=n x^(n-1)for"\ "a l l"\ "n in Ndot`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-REVISION EXERCISE
  1. If the derivative of tan^(-1)(a+b x) takes the value 1 at x=0, prove t...

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  2. Using the fact that s in (A + B) = s in A cos B + cos A s in Band the ...

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  3. If sqrt(y+x) +sqrt(y-x) =c show that dy/dx = y/x -sqrt((y^2/x^2)-1)

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  4. if sinx=ysin(x+b) show that (dy)/(dx)=(sinb)/(sin^2(x+b))

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  5. If xsin(a+y)+sinacos(a+y)=0,p rov et h a t (dy)/(dx)=(sin^2(a+y))/(si...

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  6. If y=xsin(a+y),p rov et h a t(dy)/(dx)=(sin^2(a+y))/(sin(a+y)-ycos(a+y...

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  7. Differentiate log[log(logx)] w.r.t. x.

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  8. if y = e^((x)^(e^x)) + x^(e^(e^x)) + e^(x^(x^e)), then dy/dx=e^((x)^(e...

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  9. y=sqrt(x+sqrt(x+sqrt(x+....+oo))). Find dy/dx

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  10. Find dy/dx when : y=x^(sinx-cosx)+(x^(2)-1)/(x^(2)+1)

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  11. If y=x^(cotx)+(2x^(2)-3)/(x^(2)+x+2), find (dy)/(dx).

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  12. If y=x^((x^(x))), prove that : dy/dx=x^(x+x^(x))[1/x+(1+logx)logx].

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  13. If y=(tanx)^((tanx)^((tanx)^...oo)), then prove that (dy)/(dx)=2 at x=...

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  14. Differentiate tanxtan2xtan3xtan4x in two ways : (i) by taking logari...

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  15. If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...

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  16. For what choices of a, b, c, if any, does the function f(x)={{:(ax^(...

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  17. If y=A e^(-k t)cos(p t+c), then prove that (d^2y)/(dt^2)+2k(dy)/(dx)+n...

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  18. Using mathematical induction prove that : d/(dx)(x^n)=n x^(n-1)for"\ "...

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  19. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+....+C(n)x^(n), then prove that : ...

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  20. If y=(ax^2)/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+c/(x-c)+1 then (y prim...

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