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Find (dy)/(dx) in the following: y=ta...

Find `(dy)/(dx)` in the following: `y=tan^(-1)((3x-x^3)/(1-3x^2)),-1/(sqrt(3))

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. y= tan^(-1)(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)) then dy...

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  2. Find (dy)/(dx) of y=(sinx)^x+sin^(-1)sqrt(x) .

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  3. Find (dy)/(dx) in the following: y=tan^(-1)((3x-x^3)/(1-3x^2)),-1/(...

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  4. Find the derivative of y=cos^(-1)((1-x^2)/(1+x^2)) , 0<x<1

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  5. Find the derivative of y=sin^(-1)(2xsqrt(1-x^2))

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  6. If y=sec^(-1)(1/(2x^2-1));0ltxlt (sqrt(2)),="" then="" find="" (dy)/(d...

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  7. Find the derivative of cos^(-1)(sinx) w.r.t. to x

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  8. Find the derivative of tan^(-1)((sinx)/(1+cosx)) w.r.t. to x

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  9. Find the derivative of sin^(-1)((2^(x+1))/(1+4^x))

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  10. Find (dy)/(dx) if x=a(theta-sintheta) and y=a(1-costheta) .

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  11. If x=asec^3theta and y=atan^3theta , find (dy)/(dx) at theta=pi/3

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  12. Find (dy)/(dx) if x=a(cost+tsint) and y=a(sint-tcost)

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  13. Find (dy)/(dx) if x=(3a t)/(1+t^3) ; y=(3a t^2)/(1+t^3)

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  14. Find (dy)/(dx) if =asec^2theta ; y=atan^3theta .

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  15. Find (dy)/(dx) if x=asqrt(cos2t) cost and y=asqrt(cos2t) sint then, fi...

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

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  17. find dy/dx if x=a cos 3 t ,   y=a sin 3 t

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  18. Differentiate logsinx w.r.t. sqrt(cosx)

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  19. Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) w.r.t. tan^(-1)x

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  20. Find derivative of (lnx)^(tanx) w.r.t. x^x .

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