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

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

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y^x+x^y=(x+y)^(x+y) find dy/dx

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  2. If x^m\ y^n=1 , prove that (dy)/(dx)=-(m y)/(n x)

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

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  4. If (sinx)^y=(cosy)^x , prove that (dy)/(dx)=(logcosy-ycotx)/(logsinx+x...

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  5. If (cosx)^y=(tany)^x , prove that (dy)/(dx)=(logtany+ytanx)/(logcosx-x...

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  6. If e^x+e^y=e^(x+y) , prove that (dy)/(dx)+e^(y-x)=0

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

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  8. If e^(x+y)-x=0 , prove that (dy)/(dx)=(1-x)/x

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  9. If y=xsin(a+y) , prove that (dy)/(dx)=(s in^2(a+y))/(sin(a+y)-y cos\ (...

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  10. If xsin(a+y)+sinacos(a+y)=0 , prove that (dy)/(dx)=(s in^2(a+y))/(sina...

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  11. If (sinx)^y=x+y , prove that (dy)/(dx)=(1-(x+y)ycotx)/((x+y)logsinx-1)

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

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

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

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

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

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

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

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

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