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

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

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If x^(y) =e^(x-y) , prve that , (dy)/(dx) =(logx)/((log ex)^(2)) .

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

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PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. Differentiate x^(sin^(-1)x) w.r.t 'x'

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

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

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  4. If y=e^(x+e^(x+e^(x+....TOoo))) prove that dy/dx=y/((1-y))

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  5. Differentiate tan ^(-1)((sqrt(1+x^2 )-1)/x) w,r,t. tan ^(-1)x

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  6. If e^y(x+1)=1, prove that (d^2y)/(dx^2)=((dy)/(dx))^2

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

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  8. If x=a(theta+sin theta) and y=a(1-costheta), find (d^2y)/(dx^2)"at"the...

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  9. A particle moves along the curve y=2/3x^3. Find the points on the curv...

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  10. A man of height 1.6m, walks at a rate of 30m/sec away from a lamp whic...

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  11. Water is leaking from a conical funnel at the rate of 5cm^3//sec. If t...

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  12. Find the approximate value of log(10)10.1 it being given that log10e=0...

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  13. The time T of of oscillation of a simple pendulum of length l is given...

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  14. If in a triangle ABC, the side c and the angle C remain constant while...

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  15. Find the interval in which f(x)=2x^3+3x^2-12x+1 is increasing.

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  16. Find the interval in which f(x)=x^3-3x^2-9x+30 is strictly increasing ...

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  17. The function f(x)=sin^4x+cos^4x increasing if :

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  18. Let f(x)=int0^xe^t(t-1)(t-2)dt, Then f decreases in the interval

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  19. If f(x)=x.e^(x(1-x)), then f(x) is

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  20. Let f(x)=3x+5 then show f(x) is strictly increasing and f^(-1)(x) exis...

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