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If f(x) = f(x) + f'(x) + f'''(x) ……..oo ...

If f(x) = f(x) + f'(x) + f'''(x) ……..`oo` also f(0) = 1 and f(x) is a differentiable function indefinitely then f(x) has the value

A

`e^(x)`

B

`e^(x//2)`

C

`e^(2x)`

D

`e^(4x)`

Text Solution

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The correct Answer is:
B
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MOTION-METHOD OF DIFFERENTIATION-EXERCISE - 2 (LEVEL-I)
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  3. If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y), then (dy)/(dx) equals

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  4. If x^(3)cos(xy) + y^(3)sin(xy) + 1 = 0 "then" (dy)/(dx) equals

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  5. If y=2^(log)2x^((2x))+(tan(pix)/4)^(4/(pix)) then ((dy)/(dx)])(x=1) is...

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  6. If x^m y^n=(x+y)^(m+n), then (dy)/(dx) is (x+y)/(x y) (b) x y (c) x/...

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  7. d//dx[tan^(-1)((sqrt(x^(2)+a^(2))+x)/(sqrt(x^(2)+a^(2))-x))^(1//2)]

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  8. d//dx[sin^(2)cot^(-1)""(1)/(sqrt((1+x)/(1-x)))] , is equal to -

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  9. If x=e^(sin^(- 1^t), y=tan^(- 1)t, then (dy)/(dx)

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  10. Find the derivative of f(tanx)wdotrdottg(secx)a tx=pi/4, where f^(prim...

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  11. The derivative of the function, f(x)=cos^(-1){(1)/(sqrt(13))(2cosx-3...

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  12. If y=sqrt(x+sqrt(y+sqrt(x+......,)))"then"(dy)/(dx)=

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  13. If f(x) = f(x) + f'(x) + f'''(x) ……..oo also f(0) = 1 and f(x) is a di...

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  14. If y = a cos (ln x)+ b sin (ln x), then x^(2)(d^(2)y)/(dx^(2))+x(dy)/...

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  15. If y = sin mx then the value of |[y,y1,y2],[y3,y4,y5],[y6,y5,y7]| wher...

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  16. If x=(1+t)/(t^3),y=3/(2t^2)+2/t ,t h e nx((dy)/(dx))^3-(dy)/(dx) is eq...

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  17. If sinx =(2t)/(1+t^2) and cot y =(1-t^2)/(2t) then the value of (d^2 x...

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