Maharashtra State BoardHSC Commerce 12th Board Exam
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Find Dy/Dx,If E X + E Y = E X − Y - Mathematics and Statistics

Sum

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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