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If x=sectheta-costheta and y=sec^n theta...

If `x=sectheta-costheta` and `y=sec^n theta- cos^n theta` then show that `(x^2+4)((dy)/(dx))^2=n^2(y^2+4)`

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. Find (dy)/(dx) if =asec^2theta ; y=atan^3theta .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. If y=e^(asin^(-1)x) then show that (1-x^2)y(n+2)-(2n+1)xy(n+1)-(n^2+a^...

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  19. Find (dy)/(dx), if x=acostheta , y=asintheta

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  20. Find (dy)/(dx) , if x=a t^2 , y=2a t

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