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If x=2costheta-cos2theta"and"y=2sintheta...

If `x=2costheta-cos2theta"and"y=2sintheta-sin2theta" Prove that"` `(dy)/(dx)=tan((3theta)/2)dot`

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ACCURATE PUBLICATION-DIFFERENTIABILITY-QUESTIONS CARRYING 4 MARKS
  1. If x=asin2t(1+cos2t)" and "y=bcos2t(1-cos2t). show that ((dy)/(dx))(t=...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Find the derivative of sec^(-1)((1)/(2x^(2)-1))" w.r.t. "sqrt(1-x^(2))...

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  20. Find (dy)/(dx) when y=(sinx)^(x)+sin^(-1)sqrt(x).

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