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Find (dy)/(dt), when y=sin^(-1)(2sqrt(t^...

Find `(dy)/(dt)`, when `y=sin^(-1)(2sqrt(t^(2)-1)/(t^(2)))`

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The correct Answer is:
`(dy)/(dx)=(2sqrt(t)-3t)/(tsqrt(t^(4)-4t+4sqrt(t)-1))`
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ARIHANT PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Topic 2 (practice question (4 mark question)
  1. Differentiate y=tan^(-1).(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-...

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  2. Differentiate y=(siny)^(sin2x)

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  3. Find (dy)/(dt), when y=sin^(-1)(2sqrt(t^(2)-1)/(t^(2)))

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  4. Find dy/dx if x^m y^n = (x/y)^(m+n)

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  5. Find (dy)/(dx), when y^(x)=x^(siny)

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  6. Find the dy/dx when cos x = sqrt ((1)/(1+t^2)), sin y = (2t)/(1+t^2)

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  7. If y=cosec^(-1)x, then find (dy)/(dx) and determine its value at x=-2.

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  8. Examine the differentiability to log|x| for all real values of x.

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  9. Find the derivative of x^(sinx) w.r.t.x.

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  10. Differentiate. sin^(-1)((2x)/(1+x^2))w.r.t.cos^(-1)((1-x^2)/(1+x^2))

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  11. If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a

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  12. Prove that , if y=logtan((pi)/(4)+(x)/(2)) , then (dy)/(dx)=secx

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  13. Differentiate y=2^(x^(2))+tan^(-1)((cosx-sinx)/(cos x+sinx)) w.r.t. x.

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  14. Write, why the function sin^(-1)((1)/(sqrt(1-x^(2)))) cannot be differ...

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  15. Prove that y=tan(x+y), then (dy)/(dx)=(1+y^(2))/(-y^(2))

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  16. Find the derivative of tan^(-1)(1+x^(2)) with respect to log(x^(2)+1)

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  17. If y=sin^(-1)((2sqrt(x^(2)-1))/(x^(2))) , then find (dy)/(dx).

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  18. Find dy/dx, sinx=(2t)/(1+t^2),tany=(2t)/(1-t^2)

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  19. If y=(x)/(x+2) then prove that x(dy)/(dx)=(1-y)y.

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  20. Find the derivative of (sinx)^(cosx) w.r.t.x.

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