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

If `e^y(x+1)=1` , show that `(d^2y)/(dx^2)=(dy/dx)^2`

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(dy)/(dx)=(1+x^2)(1+y^2)

V PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If y=ae^(mx)+be^(nx) , show that (d^2y)/(dx^2)-(m+n)dy/dx+mny=0

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  2. If y=500e^(7x)+600e^(-7x). Show that (d^2y)/(dx^2)=49y

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

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  4. If y=(tan^(-1)x)^2, show that (x^2+1)^2y2+2x(x^2+1)y1=2 .

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  5. Verify Rolle's theorem for the function f(x)=x^2+2 in the interval [...

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  6. Verify Mean Value Theorem for the function f(x)=x^2 in the interval [2...

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  7. Verify Rolle's Theorem for the function f(x)=x^2+2x-8 , x in [-4,2]

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  8. If f:[-5,5]toR is a differentiable function and if f'(x) does not vani...

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  9. Verify mean value theorem for the function f(x)=x^2-4x-3 in the interv...

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  10. Verify Lagrange 's mean value theorem, if f(x)=x^3-5x^2-3x in the inte...

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  11. Differentiate w.r.t. x, the following functions: (i) sqrt(3 x+2)+1/(s...

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  12. Differentiate the following w.r.t. x (i) cos ^(-1)(sin x) (if) tan ^...

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  13. Find f'(x) if f(x)=(sin x)^(sin x) for all 0ltxltpi

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  14. For a positive constant a find (dy/dx), where y=a^(t+1/t), and x=(t+1/...

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  15. Differentiate sin ^2 x w.r.t e^(cos x)

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  16. Differentiate w.r.t x the function (3 x^2-9 x+5)^9

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  17. Differentiate w.r.t x the function sin ^3 x+cos ^6 x

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  18. Differentiate w.r.t x the function (5 x)^(3 cos 2 x)

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  19. Differentiate w.r.t x the function sin ^(-1)(x sqrt(x)), 0 le x le 1

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  20. Differentiate w.r.t x the function cos ^(-1)(x/2)/(sqrt(2 x+7))

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