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

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

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If (sinx)^y=x+y , prove that (dy)/(dx)=(1-(x+y)ycotx)/((x+y)logsinx-1)

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  2. If (x-y) \ e^(x/(x-y))=a , prove that y(dy)/(dx)+x=2y .

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

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  4. Find the derivative of the function f(x) given by f(x)=(1+x)(1+x^2)...

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  5. If y=log((x^2+x+1)/(x^2-x+1))+2/(sqrt(3))t a n^(-1)((sqrt(3)x)/(1-x^2)...

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  6. If y=(sinx-cosx)^(sinx-cosx) ,pi/4 ltxlt (3pi)/ 4 find dy/dx

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  7. If x y=e^(x-y) , find (dy)/(dx) .

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  8. If y^x+x^y+x^x=a^b , find (dy)/(dx) .

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  9. If (cosx)^y=(cosy)^x find (dy)/(dx) .

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  10. If cosy=xcos(a+y) , where cosa!=-1 , prove that (dy)/(dx)=(cos^2(a+y))...

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  11. If (x-y) \ e^(x/(x-y))=a , prove that y(dy)/(dx)+x=2y .

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

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

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  14. If y=1+alpha/((1/x-alpha))+(beta//x)/((1/x-alpha)(1/x-beta))+(gamma//...

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

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

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  17. "If "y=a^(x^(a^(x...oo)))", prove that "(dy)/(dx)=(y^(2)(logy))/(x[1-y...

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  18. If y=e^(x+e^(x+e^(x+dotto\ oo))) , show that (dy)/(dx)=y/(1-y) .

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

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

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