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If x=asin2t(1+cos2t) and y=bcos2t(1-cos2...

If `x=asin2t(1+cos2t)` and `y=bcos2t(1-cos2t),` show that at `pi/4,(dy)/(dx)=b/adot`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If x=10(t-sint) , y=12(1-cost) , find (dy)/(dx) .

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  2. If x=a(theta-sintheta) and, y=a(1+costheta) , find (dy)/(dx) at theta=...

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

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

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  5. If x=(1+logt)/(t^2),y=(3+2logt)/t ,"f i n d"(dy)/(dx)dot

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  6. If x=3sint-sin3t ,y=3cos t-cos3t ,"f i n d"(dy)/(dx)"a t"t=pi/3dot

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  7. If sinx=(2t)/(1+t^2) , tany=(2t)/(1-t^2) , find (dy)/(dx) .

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  8. Differentiate logsinx with respect to sqrt(cosx) .

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  9. Differentiate tan^(-1)((1+2x)/(1-2x))w i t hr e s p e c ttosqrt(1+4x^2...

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

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

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  12. Differentiate x^x with respect to xlogx .

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  13. Differentiate tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x...

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

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  15. If x in (1/(sqrt(2)),\ 1) , differentiate tan^(-1)((sqrt(1-x^2))/x) wi...

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  16. Differentiate tan^(-1)((2x)/(1-x^2)) with respect to x

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  17. Differentiate tan^(-1)((2x)/(1-x^2)) with respect to x

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  18. Differentiate sin^(-1)((2x)/(1+x^2))

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  19. If -1/(sqrt(3))<x<1/(sqrt(3)) , differentiate tan^(-1)((3x-x^3)/(1-3x^...

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  20. Differentiate x^2 with respect to x^3 .

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