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If x=asin2t(1+cos2t)" and "y=bcos2t(1-co...

If `x=asin2t(1+cos2t)" and "y=bcos2t(1-cos2t)`. show that `((dy)/(dx))_(t=(pi)/(4))=(b)/(a)` Also find `(dy)/(dx)` at `t=pi/3`

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x= a sin 2t(1 + cos2t) and y = b cos 2t(1- cos 2t) , show that [(dy/dx)_(t=pi/4) =b/a] .

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ACCURATE PUBLICATION-DIFFERENTIABILITY-QUESTIONS CARRYING 4 MARKS
  1. Find the value of (dy)/(dx) at theta=(pi)/(4) if x=ae^(theta)(sintheta...

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  2. If x=cost(3-2cos^(2)t) and y=sint(3-2sin^(2)t), find the value of (dy)...

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  3. If x=asin2t(1+cos2t)" and "y=bcos2t(1-cos2t). show that ((dy)/(dx))(t=...

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  4. Find (dy)/(dx) at t=(pi)/(4),(pi)/(3), when x=a(cost+log"tan"(t)/(2)),...

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  5. If x=2costheta-cos2theta"and"y=2sintheta-sin2theta" Prove that" (dy...

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  6. If y=x^(sinx-cosx)+(x^(2)-1)/(x^(2)+1), find (dy)/(dx).

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  7. Find dy/dx when : y = x^(cotx) +(2x^2-3)/(x^2+x+2)

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  8. Find (dy)/(dx), if y=(cosx)^(x)+(sinx)^((1)/(x)).

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  9. If (cosx)^(y)=(siny)^(x), then find (dy)/(dx).

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  10. If y=x^(cotx)+(sinx)^(x), find (dy)/(dx).

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  11. Differentiate (sinx)^(x)+(cosx)^(sinx) w.r.t. x.

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  12. Differentiate sin^-1(2^(x+1)/(1+4^x)) w.r.t x

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  13. Differentiate the following with respect to x: sin^-1[(2^(x+1).3^x)/...

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  14. If y=cos^(-1)((2^(x+1))/(1+4^(x))), find (dy)/(dx).

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  15. If y = sin^(-1) ((2x)/(1 + x^2)) + sec^(-1) ((1 + x^2)/(1 - x^2)) , pr...

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  16. If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(...

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  17. If y = sin^-1[xsqrt(1-x) - sqrtx (sqrt(1-x^2))] find dy/dx

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

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  19. Differentiate tan^(-1)((sqrt(1 - x^2))/(x)) w.r.t. cos^(-1)(2x sqrt(1 ...

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  20. Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) w.r.t. sin^(-1)(2xsqrt(1-x...

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