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If `x = a (cos t + t sin t) y = a (sin t - t cos t)` find `(d^2y)/(dx^2)`.

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The correct Answer is:
`1/(at) "sec"^(3) t`
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SUBHASH PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -THREE MARKS QUESTIONS WITH ANSWERS
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  2. x = 2at^(2), y = at^(4).

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  3. x = a cos theta, y = b sin theta.

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  4. x = sin t, y = cos 2 t.

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  5. x = 4t, y = 4/t then find dy/dx

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  6. x = cos theta - cos 2 theta, y = sin theta - sin 2 theta. then find dy...

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  7. If x=a(theta-sin theta) and y=a(1+cos theta), then proe that (dy)/(dx)...

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  8. x = (sin^3t)/(sqrt(cos 2t)), y = (cos^3 t)/(sqrt(cos 2t)).

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  9. Find (dy)/(dx)," if "x=a(cos t+log tan""t/2), y=a sin t.

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  10. x = a sec theta, y = b tan theta.

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  11. x = a (cos theta + theta sin theta), y = a (sin theta - theta cos thet...

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  12. If x=a(theta+sin theta), y=a(1-cos theta) then show that (dy)/(dx)=tan...

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  13. If a function f(x) is differentiable at x = c prove that it is contin...

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  14. Differentiate with respect to x: (sin x)^(x) + sin^(-1)sqrt(x)

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  15. Find (dy)/(dx) given x^(y) + y^(x) = 1

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  16. If xsqrt(1 + y) + ysqrt(1 + x) = 0 x != y prove that (dy)/(dx) = (-1)/...

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  17. y = sin^(-1) x + sin^(-1)sqrt(1 - x^2), 0 lt x lt 1 find (dy)/(dx).

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  18. If cos y = x cos (a + y) with cos a != +- 1. Prove that (dy)/(dx)=co...

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  19. If x = a (cos t + t sin t) y = a (sin t - t cos t) find (d^2y)/(dx^2).

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  20. If x^(y) = e^(x - y) prove that (dy)/(dx) = (log(e)x)/((1 + log(e)x)^(...

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