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If y = cos ax, prove that |(y,y1,y2),(y3...

If `y = cos ax`, prove that `|(y,y_1,y_2),(y_3,y_4,y_5),(y_6,y_7,y_8)|=0` where `y_r=d^r/(dx^r).y`

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If y=sin mx the value of the determinant |{:(y,y_(1),y_(2)),(y_(3),y_(4),y_(5)),(y_(6),y_(7),y_8):}| where y_(n)=(d^(n)y)/(dx^(n)) is

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If y = sin mx then the value of |[y,y_1,y_2],[y_3,y_4,y_5],[y_6,y_5,y_7]| where y shows the order of derivative) is

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If y=sinm x , then the value of the determinant |y y_1y_2y_3y_4y_5y_6y_7y_8|,w h e r ey_n=(d^n y)/(dx^n) is m^9 b. m^2 c.m^3 d. none of these

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A DAS GUPTA-Differentiation-Exercise
  1. Prove that d/(dx)|(u1,v1,w1),(u2,v2,w2),(u3,v3,w3)|=|(u1,v1,w1),(u2,v2...

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  2. If fr(x),gr(x),hr(x),r=1,2,3 are polynomials such that fr(a)=gr(a)=h ,...

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  3. If y = cos ax, prove that |(y,y1,y2),(y3,y4,y5),(y6,y7,y8)|=0 where yr...

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  4. Let Delta(x)=|(x^2-1,x+1,x-2),(2x^2-1,3x,3x-3),(x^2+4,2x-1,2x-1)|. Pro...

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  5. If y=sin(2sin^-1x)show that (1-x^2)(d^2y)/(dx^2)= xdy/dx-4y

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  6. If y=a cos (logx)+b sin (logx), prove that x^(2)y(2)+xy(1)+y=0.

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  7. If y=x^(n-1) log x, prove that (x^2y2)+(3-2n)xy1+(n-1)^2.y=0 where y1...

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  8. Let y=tan^-1sqrt(x^2-1). Prove that (2x^2-1)((dy)/(dx))+x(x^2-1)((d^2...

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  9. If y=(a x+b)/(x^2+c), prove that (2x y1+y)y3=3(x y2+y1)y2.

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  10. Let y=f(x).phi(x) and z=f'(x).phi'(x). prove that 1/y*(d^2y)/(dx^2)=1/...

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  11. Let f(x+y)=f(x)dotf(y) for all xa n dydot Suppose f(5)=2a n df^(prime)...

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  12. Let f'(x) exists for all x != 0 and f(xy) = f(x) + f(y) for all real x...

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  13. A function f is defined such that for all real x, y (a) f(x+y)=f(x).f(...

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  14. A function f is defined such that for all real x, y (a) f(x+y)=f(x).f(...

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  15. Let f(x+y)=f(x)+f(y) for all real x,y and f'(0) exists. Prove that f'(...

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  16. Let f((x+y)/(2))=1/2 |f(x) +f(y)|for all real x and y, if f '(0) exist...

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  17. A function f(x) is so defined that for all real x,{f(x)}^n = f(nx). Pr...

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  18. Prove that the derivative of (a) an odd function is an even function;

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  19. Prove that the derivative of a periodic function of period T is a peri...

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  20. Let f(x) be a function satisfying the condition f(-x) = f(x) for all r...

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