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y=x^(x^(x^------infty) then prove that d...

`y=x^(x^(x^------infty)` then prove that `dy/dx=(y^2)/(x(1-ylogx))`

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If y=x^(x^(x^(...oo))) , then prove that, (dy)/(dx)=(y^(2))/(x(1-y log x)) .

If ye^y=x prove that (dy)/(dx)= y/(x(1+y))

If ye^(y)=x , prove that, (dy)/(dx)=(y)/(x(1+y)) .

(dy)/(dx)=(y(y+x))/(x(y-x))

(dy)/(dx)=(y-x)/(x+y)

If y=(x)/(x+2) prove that x(dy)/(dx)=y(1-y)

If x= e^(cos2t) and y = e^(sin2t) , then move that (dy)/(dx) = -(ylogx)/(xlogy) .

If sqrt(1-x^6)+sqrt(1-y^6) = a(x^3-y^3) then prove that (dy)/(dx)= x^2/y^2sqrt((1-y^6)/(1-x^6))

(dy)/(dx)=(3x+2y)/(2x-3y)

(dy)/(dx)=(2x-3y)/(3x-2y)

PATHFINDER-DERIVATIVES-QUESTION BANK
  1. If log(x^2-y^2)/(x^2+Y^2)=a the prove that (dy/dx)=y/x

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  2. prove that d/dx(x^x)=x^x(1+logex)

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  3. y=x^(x^(x^------infty) then prove that dy/dx=(y^2)/(x(1-ylogx))

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  4. If y=tan^(-1)(5ax)/(a^2-6x^2) prove that dy/dx=(3a)/(a^2+9x^2)+(2a)/(a...

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  5. y=sin^(-1)(xsqrt(1-x)+sqrtxsqrt(1-x^2)) show that dy/dx=(1)/(sqrt(1-x^...

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  6. f(x) is differentiable at x=a prove that underset(xrarra)Lt ((x+a)f(a)...

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  7. If y=g{g(x)}, g(0)=0 and g'(0)=2 then find dy/dx at x=0

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  8. 2f(x)+3f(-x)=x^2-x+1 then determine f'(1)

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  9. x=sectheta-costheta , y=sec^n theta- cos^n theta show that (dy/dx)^2=(...

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  10. y=tan^(-1) ((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)) show that dy/d...

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  11. f(x)=5x-4 (0ltxle1) =4x^2-3x (1ltxlt2) test whether f(x) is differenti...

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  12. find the derivative of x^x

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  13. Find by the defination the differential coefficient of the following: ...

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  14. Find derivative of the following: sec3x

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  15. Find derivative of the following:e^(sqrtx)

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  16. Find derivative of the following: sin^(-1)x

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  17. Find by the definition the differential coefficient of the following: ...

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  18. Find by the definition the differential coefficient of the following:l...

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  19. Find by the definition the differential coefficient of the following: ...

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  20. Find by the definition the differential coefficient of the following: ...

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