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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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The correct Answer is:
`=((1+log y)^2)/(log y)`
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If y^(x) = e^(y -x) , prove that (dy)/(dx) = ((1 + log y)^2)/(log y) .

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OSWAAL PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-DIFFERENTIABILITY ( LONG ANSWER TYPE QUESTIONS-I)
  1. Differentiate the following function with respect to x : (log"\ x...

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  2. If x=asint\ and y=a(cost+logtant/2) , find (d^2\ y)/(dx^2)

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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 siny=xsin(a+y), prove that (dy)/(dx)=(sin^2(a+y))/(sina)

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  5. If xsin(a+y)+sinacos(a+y)=0,p rov et h a t (dy)/(dx)=(sin^2(a+y))/(si...

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  6. Differentiate the following with respect to x : sin^(-1)((2^(x+1). 3^x...

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  7. If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(...

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  8. If y= x^(sin x- cos x)+ (x^(2)-1)/(x^(2)+1)," find "(dy)/(dx).

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  9. If y=x^(cotx)+(2x^(2)-3)/(x^(2)+x+2), find (dy)/(dx).

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  10. If x=cost+logtant/2,\ \ y=sint , then find the value of (d^2y)/(dt^2) ...

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

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  12. If y=(t a n^(-1)\ x^2) , show that (x^2+1)^2(d^2\ y)/(dx^2)+2x(x^2+1)(...

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  13. If y=3cos(logx)+4sin(logx),\ then show that x^2dot(d^2\ y)/(dx^2)+...

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  14. If y=sin^(-1)x, show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0.

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  15. Differentiate tan^(-1)[(sqrt(1+x^2)-1)/x] with respect to x

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  16. If x=a(cos t+t\ s in\ t) and y=a\ (sint-t\ cos t),\ \ then find (d^2\...

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  17. Differentiate tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x...

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  18. If y=(sin^(-1)x)/(sqrt(1-x^2)) , show that (1-x^2)(d^2y)/(dx^2)-3x(dy)...

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  19. If x=a(theta-sintheta) and, y=a(1+costheta) , find (dy)/(dx) at theta=...

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  20. If y=logsqrt((1+tanx)/(1-tanx)),"P r o v et h a t"(dy)/(dx)=sec2x

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