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Question
Find `dy/dx,if e^x+e^y=e^(x-y)`
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Solution
`e^x + e^y = e^(x – y)`
diff. w.r.t. x
`(de^x)/dx+(de^y)/dx=(de(x-y))/dx`
`e^x + e^y dy/dx=e^(x-y) (1-dy/dx)`
`(e^y + e^(x – y))dy/dx=e^(x-y)-e^x`
`dy/dx=((e^(x-y)-e^x)/(e^(x-y+e^y)))=(e^x+e^y-e^x)/(e^x+e^y+e^y)`
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