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If 2^x+2^y=2^(x+y), then dy/dx is equal ...

If `2^x+2^y=2^(x+y)`, then dy/dx is equal to :

A

`((2^x+2^y)/(2^x-2^y))`

B

`((2^x+2^y))/((1+2^(x+y)))`

C

`2^(x-y)((2^y-1)/(1-2^x))`

D

`(2^(x+y)-2^x)/2^y`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • If y^x=x^y , then dy/dx is equal to

    A
    `(y-xlogy)/(x-ylogx)`
    B
    `-((y-xlogy)/(x-ylogx))`
    C
    `-y/x((y-xlogy)/(x-ylogx))`
    D
    `y/x((y-xlogy)/(x-ylogx))`

  • If x^2+2xy+y^3=42 , then dy/dx is equal to

    A
    `(-2(x+y))/(2x+3y^2)`
    B
    `(-2(x+3y^2))/(2(x+y))`
    C
    `(-2(x+y))/(2y+3x^2)`
    D
    `(2(x^2+y^2))/(2x+3y^2)`

  • If y^(x) = x^(y) , "then" (dy)/(dx) is equal to

    A
    `(y)/(x) ((y + x logy)/(x - y logx))`
    B
    `(y)/(x) ((y - x logy)/(x - y logx))`
    C
    `(y)/(x) ((y + x logy)/(x + y logx))`
    D
    None of these

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