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If x= 3 sin t- sin (3t), y= 3 cos t- cos...

If `x= 3 sin t- sin (3t), y= 3 cos t- cos 3t`, then find `((dy)/(dx)) " at " t= (pi)/(3)`

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The correct Answer is:
`-(1)/(sqrt3)`
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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-NCERT Exemplar Problems and Solution (Short Answer Type Questions)
  1. Find (dy)/(dx): x= e^(cos 2t) and y= e^(sin 2t) show that, (dy)/(dx)...

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  2. Find (dy)/(dx): x=a sin 2t (1+ cos 2t) and y= b cos 2t (1-cos 2t) ...

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  3. If x= 3 sin t- sin (3t), y= 3 cos t- cos 3t, then find ((dy)/(dx)) " ...

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  4. Differentiate (x)/(sin x) w.r.t sin x

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

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  6. Find (dy)/(dx) when x and y are connected by the relation given: si...

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  7. Find (dy)/(dx) when x and y are connected by the relation given: se...

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  8. Find (dy)/(dx) when x and y are connected by the relation given: ta...

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  9. Find (dy)/(dx) when x and y are connected by the relation given: (x...

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  10. If ax^(2) + 2hxy + by^(2) + 2gx + 2f y + c = 0, then show that (dy)/(d...

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  11. If x= e^((x)/(y)), then prove that (dy)/(dx)= (x-y)/(x.log x)

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  12. If y^(x)= e^(y-x), then prove that (dy)/(dx)= ((1+ log y)^(2))/(log y)

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  13. If y= (cos x)^((cos x)^((cos x)……oo)), then show that (dy)/(dx)= (y^(2...

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  14. If x sin (a + y) + sin a cos (a + y)= 0, then prove that (dy)/(dx)= (s...

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  15. If sqrt(1-x^(2)) + sqrt(1 -y^(2))= a(x-y), then prove that (dy)/(dx)= ...

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  16. If y= tan^(-1)x, then find (d^(2)y)/(dx^(2)) in terms of y alone.

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  17. Verify the Rolle's theorem for each of the function in following quest...

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  18. Verify the Rolle's theorem for each of the function in following quest...

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  19. Verify the Rolle's theorem for each of the function in following quest...

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  20. Verify the Rolle's theorem for each of the function in following quest...

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