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Find the derivative of cos^(-1)(sqrt(1+x...

Find the derivative of `cos^(-1)(sqrt(1+x)/2)`.

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SHARAM PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXAMPLE
  1. What is the derivative of tan ^(-1)(cos sqrt(x)).

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  2. If y=cot^(-1)(sqrt(1+x^2)/x) then (dy)/(dx)=?

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  3. Find the derivative of cos^(-1)(sqrt(1+x)/2).

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  4. Differentiate cos^(-1) (4x^3-3x).

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  5. Differentiate tan^(-1)((sqrtx-x)/(1+xsqrt(x))).

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  6. If y=10^(x) and z=100^(x/2) then find d/dx(y^(2)/z).

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  7. What is the derivative of cos (sin^(-1)x) w.r.t cos^(-1)x?

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  8. What is the derivative of cosec^(-1) x w.r.t x when |x|>1.

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  9. Find (dy)/(dx)when y = log|x|.

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  10. Find (dy)/(dx) att = 1/2 when x = (at^2), y=2at.

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  11. Find d/(dx) In sin^(-1)cos((pi-2e^x)/2).

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  12. If y=tan^(-1)((a)/(x))+logsqrt((x-a)/(x+a)), then prove that (dy)/(dx)...

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  13. If (tan^(-1)x)^y + y^(cotx) =1then find (dy)/(dx).

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

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

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

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

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

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

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

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