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If y=(sin^(-1)x)^2, then prove that (1-x...

If `y=(sin^(-1)x)^2`, then prove that `(1-x^2)y_2-xy_1=2`

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MAHAVEER PUBLICATION-DIFFERENTIATION OR DERIVATIVE OF A FUNCTION-QUESTION BANK
  1. Find (d^2y)/(dx^2) at x=2 if y=x^3+logx

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  2. If y=Acos sqrtkx+Bsin sqrtkx, prove that y2+ky=0

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  3. If y=(sin^(-1)x)^2, then prove that (1-x^2)y2-xy1=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. If y=ae^(3x), then prove that (d^2y)/(dx^2)=9y.

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  6. If y=e^(ax)cosbx, then prove that : (d^(2)y)/(dx^(2))-2ady/dx+(a^(2)...

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  7. Without using derivative, find the maximum value and the minimum value...

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  8. Without using derivative, find the maximum value and the minimum value...

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  9. Without using derivative, find the maximum value and the minimum value...

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  10. Find the local maximum, local minimum, absolute maximum and absolute m...

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  11. Find the local maximum, local minimum, absolute maximum and absolute m...

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  12. Find the local maximum, local minimum, absolute maximum and absolute m...

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  13. Show that f(x)=x^3-6x^2+24x+4 has neither maxima nor minima.

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  14. Find from the Definition of Derivative: f'(pi/4) where f(x)=secx

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  15. Find the derivatives of the followings from the 1^(st) principle. x^2+...

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  16. Find the derivatives of the followings from the 1^(st) principle. x/(1...

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  17. Find the derivatives of the followings from the 1^(st) principle. cos^...

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  18. Examine the differentiability at x=0 and x=1: f(x)={(-x, xlt0),(x^2, 0...

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  19. Examine the differentiability at x=0,1,2 if: f(X)={(4-x, xle0),(5x+4, ...

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  20. Find the sum 1+2x+3x^2+…..+nx^(n-1) from the relation 1+x+x^2+x^3+…..+...

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