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If y=e^(x+e^(x+e^((((( tooo))))))),show...

If `y=e^(x+e^(x+e^((((( tooo))))))),`show that`(dy)/(dx)=y/(1-y)`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))),prove that (dy)/(dx)=(cosx...

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  2. If y=a^(x^(a^(x^......)^oo))), \ p rov et h a t \ (dy)/(dx)=(y^2logy...

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  3. If y=e^(x+e^(x+e^((((( tooo))))))),show that(dy)/(dx)=y/(1-y)

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  4. If y=(sqrt(x))^sqrt(x)^sqrt(x)^(dot)^(((oo))),s howt h a t(dy)/(dx)=(y...

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  5. If y=x+1/(x+1/(1/(x+))), p rov et h a t(dy)/(dx)=y/(2y-x)

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  6. If y=(sinx)/(1+(cosx)/(1+(sinx)/(1+(cosx)/(1+ tooo)))),p rov et h a t(...

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  7. If e^x+e^y=e^(x+y), prove that (dy)/(dx)=-(e^x(e^y-1))/(e^y(e^x-1))

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  8. If y=(cosx)^((((cosx)^(((cosx)^((...oo)) prove that (dy)/(dx)=-(y^2tan...

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  9. If y=sqrt(sinx+y) ,write (dy)/(dx)dot

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  10. If y=x^x^x^ddot^((((oo)))), (dy)/(dx) is

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  11. If y=x^(tanx)+sqrt((x^2+1)/2),fin d(dy)/(dx)

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  12. If x^y=y^x ,then find (dy)/(dx)

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  13. If (sin"x")^y=(cos"y")^x, prove that (dy)/(dx)=(logcosy-ycotx)/(logsin...

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  14. If y^(x)=e^(y-x), then prove that (dy)/(dx) = ((1+logy)^(2))/(logy)

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  15. If y=(ax^2)/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+c/(x-c)+1 then (y prim...

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  16. If x=e^(x/y),prove that(dy)/(dx)=(x-y)/(xlogx)

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  17. If y=xsiny, prove that (dy)/(dx)=y/(x(1-xcosy)

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  18. If x ylog(x+y)=1, prove that (dy)/(dx)=-(y(x^2y+x+y))/(x(x y^2+x+y))

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  19. If (sin"x")^y=x+y ,p rov et h a t(dy)/(dx)=(1-(x+y)ycotx)/((x+y)logsin...

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  20. Differentiate: (logx)^x+x^(logx)w i t hr e s p e c t to x :

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