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

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

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. If x=asec^3theta and y=atan^3theta , find (dy)/(dx) at theta=pi/3

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

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

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

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

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

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

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

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

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

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  11. Derivative of cos^(-1)(2x^2-1) w.r.t. sqrt(1-x^2) when x=1/2 .

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  12. Define derivative of sin^(-1)((2x)/(1+x^2)) w.r.t. cos^(-1)((1-x^2)/(1...

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  13. Differential coefficient of e^sin^((-1)x) w.r.t. e^-cos^((-1)x) is ind...

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  14. Find the derivative of f(tanx) w.r.t. g(secx) at x=pi/4 , where f^(pri...

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  15. If y=sin(sinx) then prove that y2+(tanx)y1+ycos^2x=0

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  16. If y=acos(lnx)+bsin(lnx) then prove that x^2y3+3x y2+2y1=0

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  17. If y=e^acos^((-1)x) , then prove that (1-x^2)y2-x y1-a^2y=0 .

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  18. If (x-a)^2+(y-b)^2=c^2\ \ (c >0) then ([1+((dy)/(dx))^2]^(3//2))/((d^2...

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  19. Using mathematical induction prove that d/(dx)(x^n)=n x^(n-1) for all...

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  20. If y=e^tan^((-1)x) , prove that (1+x^2)y2+(2x-1)y1=0 .

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