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If x= e^(cos2t) and y = e^(sin2t), the...

If `x= e^(cos2t)` and `y = e^(sin2t)`, then move that `(dy)/(dx) = -(ylogx)/(xlogy)`.

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Find (dy)/(dx) , when x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2)

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  2. If x=2costheta-cos2theta"and"y=2sintheta-sin2theta"P r o v et h a t" ...

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  3. If x= e^(cos2t) and y = e^(sin2t), then move that (dy)/(dx) = -(yl...

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  4. If x=cost " and " y=sint ,"prove : "(dy)/(dx)=1/(sqrt(3))"at " t=(2pi)...

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  5. x = t + (1)/(t), y = t - 1/t

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  6. If x=sin^(-1)((2t)/(1+t^2))"and"y=tan^(-1)((2t)/(1-t^2)),-1<t<1, "p r...

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  7. If x and y are connected parametrically by the equations given, witho...

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  8. If a>0, x=(t+1/t)^a ,y=a^(t+1/t),"find " (dy)/(dx)

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  9. If x=a((1+t^2)/(1-t^2))"and"y=(2t)/(1-t^2),"f i n d"(dy)/(dx)

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  10. If x=10(t-sint) , y=12(1-cost) , find (dy)/(dx) .

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

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

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

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

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

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

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

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

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

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

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