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Find dy/dx, when x log x + y log y + x...

Find `dy/dx`, when
x log x + y log y + xy - 5x + 2y + 3 = 0

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PATHFINDER-BASIC MATHEMATICS-QUESTION BANK
  1. Differentiate the following functions : (cos^-1(1-3x))^2

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  2. Find dy/dx, when x=acos t + at, y = asin t -at, where t is the param...

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  3. Find dy/dx, when x log x + y log y + xy - 5x + 2y + 3 = 0

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  4. Find dy/dx, when y = x^x+(sin x )^(cosx)

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  5. If the radius of a circle changes at a uniform rate of 2 cm/s, find th...

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  6. A particle is moving in a vertical line whose equation of motion is gi...

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  7. Find the equation of the tangent and the normal at the point (0, -1) t...

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  8. For the function f(x) = 2x^3-8x^2+10x+5, find the interval (s) in wh...

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  9. For the function f(x) = 2x^3-8x^2+10x+5, find the interval (s) in wh...

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  10. Investigate the increasing or decreasing behaviour of the following fu...

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  11. If xgt0,ygt0 and x+y=1, then find the minimum value of x log x + y log...

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  12. Evaluate the following integrals : intx.e^xdx

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  13. Evaluate the following integrals : inte^(tan^-1x)/(1+x^2)dx

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  14. Evaluate the following integrals : intsecx(secx+tanx)dx

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  15. Evaluate the following integrals : int3^6abs(x-4)dx

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  16. Solve the following differential equations : xdy+ydx=0,at x=1,y=1

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  17. Solve the following differential equations : dy/dx+sqrt((1-y^2)/(1-x...

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  18. Solve the following differential equations : tan x cdotcos^2ydx+tan ...

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  19. Solve the following differential equations : x(1+y^2)dx+y(1+x^2)dy=0...

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  20. Let{x} and [x] denote the fractional and integral parts of a real numb...

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