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If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ too...

If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))),p rov et h a t(dy)/(dx)=(cosx)/(2y-1)`

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To solve the problem, we start with the given expression for \( y \): \[ y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \ldots}}} \] ### Step 1: Rewrite the expression ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If x=asec^3theta and y=atan^3theta, find (dy)/(dx) at theta=pi/3

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  2. If x=sin^(-1)((2t)/(1+t^2))a n dy=tan^(-1)((2t)/(1-t^2)),t > 1. P rov ...

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  3. If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))),p rov et h a t(dy)/(dx)=(...

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

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  5. If y=e^x^+e^x^+e^((((( tooo))))),s howt h a t(dy)/(dx)=y/(1-y)

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

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

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

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

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

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  11. If y=sqrt(sinx+y),then find (dy)/(dx)dot

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

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  13. If y=x^(tanx)+sqrt((x^2+1)/2),find(dy)/(dx)

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

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  15. If (sin"x")^y=(cos"y")^x ,p rov et h a t(dy)/(dx)=(logcosy-ycotx)/(log...

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

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  17. If y=(a x^2)/((x-a)(x-b)(x-c))+(b x)/((x-b)(x-c))+c/(x-c)+1 find dy/dx

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

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

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

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