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If f(1) = 3 ,f'(1)=-1/3 , then the deriv...

If `f(1) = 3 ,f'(1)=-1/3` , then the derivative of `{x^(11) +f(x)}^(-2)` at x = 1 is

A

`-1/2`

B

`-1`

C

1

D

`f^(1)(1)`

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The correct Answer is:
D
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AAKASH SERIES-DIFFRENTATION-PRACTICE SHEET (EXERCISE - I) (LEVEL - I)(Straight Objective Type Questios)
  1. sqrt((y)/( x))+ sqrt((x)/(y))= 2 implies (dy)/(dx) =

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  2. If f(x) = (ax + b) Cos x +(cx +d) Sin x and f^(1) (x) = x Cosx is an a...

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  3. If f(1) = 3 ,f'(1)=-1/3 , then the derivative of {x^(11) +f(x)}^(-2) a...

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  4. Let f(x+y)=f(x)f(y) and f(x) = 1 + (sin2x) g(x) where g(x) is continu...

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  5. If y = f((3x+4)/(5x+6)) and f^(1)(x) = tanx^2 then (dy)/(dx) is equal...

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  6. If y =a sin x + b cos x , then y^2 + ((dy)/(dx))^2 is a

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  7. Let h(x) be differentiable for all x and let f(x) = (kx+e^(x)),h(x) wh...

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  8. d/(dx){Tan^(-1)((asinx + b cosx)/(acosx-bsinx))} =

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  9. d/(dx)[tanh^(-1)((2x)/(1+x^2))]=

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  10. If g is the inverse of f and f'(x) = 1/(2+x^n) , then g^(1)(x) is equa...

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  11. The derivative of sin^(-1)((2x)/(1+x^2)) with respect to cos^(-1)((1-x...

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  12. If y = Sin ^(-1) (1 - x ^(2))/(1+ x ^(2)) then (dy)/(dX)=

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  13. If y = cos^(-1)((a^(2)-x^(2))/(a^(2)+x^(2)))+sin^(-1)((2ax)/(a^(2)+x^(...

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  14. y = Cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))] ...

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  15. If sin^(-1)((x^2-y^2)/(x^2+y^2)) = loga , then (dy)/(dx) is equal to

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  16. The derivative of Sec ^(-1)"" (1)/( 2x ^(2) -1) w.r.t . sqrt(1+ 3x ) a...

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  17. If r = [ 2 phi +cos^2(2phi+pi//4)]^(1//2) , then what is the value of ...

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  18. If y =cot^(-1) (1-x+x^2) , then (dy)/(dx) =

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  19. f(x) = Cot^(-1)((x^x-x^(-x))/(2)) then f^(1)(1)=

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  20. f(x) = Cot^(-1)((x^x-x^(-x))/(2)) then f^(1)(1)=

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