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Prove that (cot^(-1)x+"cot"^(-1)1/x) is ...

Prove that `(cot^(-1)x+"cot"^(-1)1/x)` is a constant.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-REVISION EXERCISE
  1. Differentiate the following w.r.t. x: e^(log(x+sqrt(x^(2)+a^(2))))

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  2. Differentiate the following w.r.t. x: e^(2logx+3x)

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  3. Prove that (cot^(-1)x+"cot"^(-1)1/x) is a constant.

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  4. If y=f((2x-1)/(x^2+1)) and f^(prime)(x)=sinx^2 , find (dy)/(dx) .

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  5. Find the derivative of the following w.e.t. x : 3/(root(3)(x))-5/cos...

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  6. Find the derivative of the following w.e.t. x : log(1/sqrtx)+5x^(a)-...

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  7. If y=tan^(-1)((e^(2x)+1)/(e^(2x)-1)), prove that : dy/dx=-(2e^(2x))/...

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  8. If the derivative of tan^(-1)(a+b x) takes the value 1 at x=0, prove t...

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

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

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

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  12. 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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  13. 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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  14. Differentiate log[log(logx)] w.r.t. x.

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

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

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

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

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

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

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