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find the derivative of e^(x) + e^(y) = ...

find the derivative of ` e^(x) + e^(y) = e^(x +y)`

A

`-e^(x-y)`

B

`e^(x-y)`

C

`-e(y-x)`

D

`e(y-x)`

Text Solution

Verified by Experts

The correct Answer is:
C
`e^(x) +e^(y)=e^(x+y)=e^(x)e^(y)`
`implies e^(-y)+e^(-x)=1 `
On differenting , we get
`-e^(-y)""(dy)/(dx)+e^(-x)(-1)=0`
` implies (dy)/(dx)=(e^(-x))/(-e^(-y))`
`implies (dy)/(dx)=-e^(y-x)`
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