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If y=x+1/(x+1/(x+1/(x+\ dot))) , prove ...

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

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To solve the problem, we start with the equation given: \[ y = x + \frac{1}{y} \] ### Step 1: Rewrite the equation We recognize that the expression for \(y\) is recursive. Thus, we can rewrite it as: ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If y=e^(x+e^(x+e^(x+dotto\ oo))) , show that (dy)/(dx)=y/(1-y) .

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  2. If y=(sqrt(x))^(sqrt(x))^(((sqrt(x))dotoo)) , show that (dy)/(dx)=(y^2...

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

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  4. If y=(sinx)/(1+(cosx)/(1+(sinx)/(1+(cosx)/(1+\ ddotto\ oo)))) , prove ...

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  5. If y=sqrt(x+sqrt(x+sqrt(x+\ dotto\ oo))) , prove that (dy)/(dx)=1/(2\ ...

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  6. If y=sqrt(cosx+sqrt(cosx+sqrt(cosx+\ dotto\ oo))) , prove that (dy)/(d...

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  7. If y=sqrt(logx+sqrt(logx+sqrt(logx+\ dotto\ oo))) , prove that (2y-1)(...

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  8. If y=sqrt(tanx+sqrt(tanx+sqrt(tanx+\ dotto\ oo))) , prove that (dy)/(d...

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  9. If y=(sinx)^(sinx^(sinx dotoo)) , prove that (dy)/(dx)=(y^2cotx)/((1-y...

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  10. cos 6x=32 cos^6 x -48cos^4 x + 18 cos^2 x -1

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  11. If y=e^x^e^x+e^x^x^e , prove that (dy)/(dx)=e^x^e^xdotx^e^x{(e^x)/x+ed...

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

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

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  14. Find (dy)/(dx): x=a(theta-sintheta) and y=a(1-costheta)

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  15. If x=a\ s e c^3theta and y=a\ t a n^3theta , find (dy)/(dx) at theta=p...

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

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

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  18. 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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  19. 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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  20. If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...

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