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If y =a sin x + b cos x , then y^2 + ((...

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

A

function of x

B

function of y

C

function of x and y

D

constant

Text Solution

Verified by Experts

The correct Answer is:
D
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AAKASH SERIES-DIFFRENTATION-PRACTICE SHEET (EXERCISE - I) (LEVEL - I)(Straight Objective Type Questios)
  1. Let f(x+y)=f(x)f(y) and f(x) = 1 + (sin2x) g(x) where g(x) is continu...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. If y =(logx)^(x) then (dy)/(dx) =

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  19. If x^(m) y^(n)=(x+y)^(m+n) , then dy/dx is equal to

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  20. If y = 2^(2 ^(x)), then (dy)/(dx) =

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