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If x=a(cost+logtant/2) , y=asint , evalu...

If `x=a(cost+logtant/2)` , `y=asint` , evaluate `(d^2y)/(dx^2)` at `t=pi/3` .

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The correct Answer is:
`(8sqrt(3))/(a)`
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OSWAAL PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-DIFFERENTIABILITY ( LONG ANSWER TYPE QUESTIONS-I)
  1. If x=a(cost+tsint) and y=a(sint-tcost) , then find the value of (d^...

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  2. If (x-y)ex/(x-y)=a , prove that (dy)/(dx)+x=2ydot

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  3. If x=a(cost+logtant/2) , y=asint , evaluate (d^2y)/(dx^2) at t=pi/3 .

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  4. If y=tan^(-1)(a/x)+logsqrt((x-a)/(x+a)) , Prove that (dy)/(dx)=(2a^3)/...

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  5. If (tan^(-1)x)^(y)+y^(cotx)=1, then find (dy)/(dx).

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  6. Differentiate tan^(-1)((sqrt(1-x^2))/x) with respect to cos^(-1)(2xsqr...

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  7. Differentiate tan^(-1)(x/(sqrt(1-x^2))) with respect to sin^(-1...

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  8. Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) with respect to sin^(-...

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  9. If y=x^x , prove that (d^2y)/(dx^2)-1/y((dy)/(dx))^2-y/x=0

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  10. Find the value of (dy)/(dx) at theta= pi/4, if x=ae^theta(sintheta-c...

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  11. If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t), show that at pi/4,(dy)/...

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  12. If x=cost(3-2\ cos^2t) and y=sint(3-2s in^2t) find the value of (dy)/(...

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  13. If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n ...

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  14. If x = a cos theta + b sin theta and y =asin theta-b cos theta, then p...

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  15. If x^my^n=(x+y)^(m+n) prove that (dy)/(dx)=y/x

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  16. Differentiate log (x^(sin x)+cot^(2) x) w.r.tx.

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  17. If x=2costheta-cos2theta and y=2sintheta-sin2theta then prove that (dy...

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  18. If y=(sinx)^x+sin^(-1)sqrt(x) then find dy/dx.

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  19. If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

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  20. If y=log{x+sqrt(x^2+a^2)} , prove that: (x^2+a^2)(d^2y)/(dx^2)+x(dy)/(...

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