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If y=e^(x^(e^x))+x^(e^(e^x))+e^(x^(x^e))...

If `y=e^(x^(e^x))+x^(e^(e^x))+e^(x^(x^e))` , prove that `(dy)/(dx)=e^(x^(e^x)) . x^(e^x){(e^x)/x+e^x.logx}+x^(e^(e^x)).e^(e^x){1/x+e^xdotlogx}+e^(x^(x^e)).x^(x^e).x^(e-1){1+elogx}`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y=sinx^(sinx^(sinx^dotoo)) , prove that (dy)/(dx)=(y^2cotx)/((1-ylo...

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  2. Prove that : cos 6x=32 cos^6 x -48cos^4 x - 18 cos^2 x -1

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  3. If y=e^(x^(e^x))+x^(e^(e^x))+e^(x^(x^e)) , prove that (dy)/(dx)=e^(x^(...

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  4. If y=cosx^(cosx^(cosx^dotoo)) , prove that (dy)/(dx)=-(y^2tanx)/((1-yl...

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  5. Find (dy)/(dx) : x=a{cost+1/2logt a n^2t/2} and y=asint .

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  6. Find (dy)/(dx), when x=a(theta+sintheta)a n dy=a(1-costheta)

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  7. If x=asec^3thetaa n dy=atan^3theta,fin d(dy)/(dx)a ttheta=pi/3dot

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  8. Find (dy)/(dx) , when x=a\ cos^3t and y=at .

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  9. If x=sqrt(a^(sin^(-1)t)), y=sqrt(a^(cos^(-1)t)) , show that (dy)/(dx)=...

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  10. If x=sin^(-1)((2t)/(1+t^2)) and y=tan^(-1)((2t)/(1-t^2)),t > 1. Prove ...

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  11. If u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt(...

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  12. If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...

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  13. Find (dy)/(dx) , when x=a t^2 and y=2\ a t

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  14. Find (dy)/(dx), when x=a(theta+sintheta)a n dy=a(1-costheta)

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  15. Find (dy)/(dx) when x = a cos theta and y = b sin theta

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  16. Find (dy)/(dx), when x=a e^(theta)(sintheta-costheta),y=a e^(theta)(si...

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  17. Find (dy)/(dx) , when x=b\ sin^2theta and y=a\ cos^2theta

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  18. Find (dy)/(dx), when x=a(theta+sintheta)a n dy=a(1-costheta)

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  19. Find (dy)/(dx), when x=(e^t+e^(-t))/2 \ a n d \ y=(e^t-e^(-t))/2

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  20. Find (dy)/(dx), when x=(3a t)/(1+t^2)" and "y =(3a t^2)/(1+t^2)

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