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If 2^(x)+2^(y)=2^(x+y), then the value o...

If `2^(x)+2^(y)=2^(x+y)`, then the value of `(dy)/(dx)` at x = y = 1 is

A

0

B

`-1`

C

1

D

2

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The correct Answer is:
B
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MCGROW HILL PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -EXERCISE (LEVEL 1) Single Correct Answer Type Questions
  1. If x=a cos 2t,y=b sin^(2)t then (d^(2)y)/(dx^(2)) is equal to

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  2. If f(x)=tan^(-1)sqrt((1+sinx)//(1-sinx)),0le x lt pi//2, then f'(pi//6...

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  3. If 2^(x)+2^(y)=2^(x+y), then the value of (dy)/(dx) at x = y = 1 is

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  4. If t=sin^(-1)2^(8) then (ds)/(dt) is equal to

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  5. Let (x, y) be any point on the unit circle with centre at the origin, ...

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  6. Let f(x) =log sinx^(2),0lt x lt pi//2 then f''(sqrt(pi)//2) is equal t...

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  7. Let g(x) be the inverse of f(x) and f'(x)=(1)/(1+x^(5)) then (d^(2))/(...

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  8. The derivative of f(tanx) with respect to g(sec x) at x =(pi)/(4), whe...

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  9. If y=(log(cosx)sinx)(log(nx)cosx)+sin^(-1)""(2x)/(1+x^(2)), then (dy)/...

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  10. If y=sin^(-1)((5x+12sqrt(1-x^(2)))/(13)), then (dy)/(dx) is equal to:

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  11. Let f:(-1,1)toR be a differentiable function with f(0)=-1 and f'(0)=1....

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  12. Let y be an implicit function of x defined by x^(2x)-2x^(x)coty-1=0. T...

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  13. Let f(x)={{:((x-1)sin""(1)/(x-1),,"if "x ne1),(0,,"if "x=1):} The wh...

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  14. Let f(x) be defined by f(x)={{:(sin2x,,"if "0lt x le pi//6),(ax+b,,"...

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  15. Let f(x)={{:(1//|x|,,"for "|x|ge1),(ax^(2)+b,,"for "|x|lt1):} The ...

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  16. For a real number y, let [y] denote the greatest integer less than or ...

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  17. If f(x)={{:((cosx)^(1//sinx),,"for "x ne0),(k,,"for "x=0):} the va...

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  18. If y=sin^(-1)((sin alpha sinx)/(1-cos alpha sin x)), then y'(0) is

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  19. The st of all poinst of differentiability of the function f(x)=(sqrt...

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  20. If x=sin^(-1)t and y=log(1-t^(2)), then (d^(2)y)/(dx^(2))|(t=1//2) is

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