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If x^y = e^(x-y) " then " dy/dx ?...

If `x^y = e^(x-y) " then " dy/dx ?`

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A DAS GUPTA-Differentiation-Exercise
  1. IF y = 1 / (1+ x + x^2 + x^3), then value of (d^2y) / dx^2 at x = 0 is

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  2. If y=log (x+5), x!= -5 then dy/dx=

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  3. If x^y = e^(x-y) " then " dy/dx ?

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  4. If x=e^tcos t,y=e^t sin t then (dy)/(dx)=

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  5. If phi(x)= |[1,2x,3x^2], [x,x^2,x^4], [0,2,6x]| then phi'(1)=

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  6. The value of (dy/dx){(1,1)} for the curve 2y = 3 -x^2 is

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  7. Let y =log(e)sin(x^2),0ltxlepi/2. The value of dy/dx at x= sqrt(pi/2) ...

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  8. If f(x) = log ex then the differential coefficent of f(logex) with res...

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  9. If y^2=P(x) is a polynomial of degree 3, then 2(d/(dx))(y^2dot(d^2y)/(...

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  10. If f(x) = tan^-1 {1/x (sqrt(1+x^2))} then f'(0) is

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  11. If t=e^x and y=t^2-1 then (dy/dx) at t=1 is

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  12. x^3-2x^2y^2+5x+y-5=0, then find (d^2y)/(dx^2) at x=1, y=1

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  13. Let f(x)=|x^3sinxcosx6-1 0p p^2p^3|,w h e r ep is a constant. Then (d...

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  14. The derivative of an even function is always an odd function.

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  15. If both f(x) and g(x) are non-differentiable at x=a then f(x)+g(x) may...

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  16. If y=f((2x-1)/(x^2+1)) and f^(prime)(x)=sinx^2 , find (dy)/(dx) .

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  17. Q.14 Let f(x) = (ax + b) cosx + (cx + d) sinx andf'(x) = x cosx for al...

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  18. If f(x) = |x - 1| and g(x) = f(f(f(x))) then for x gt 2, g'(x) =

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  19. (d(x^(logx)))/(d(logx))=

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  20. Find dy/dx in terms of x if t= x/(1+x^2), y=x^2+t^2.

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