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If e^(x+y)-x=0 , prove that (dy)/(dx)=(1...

If `e^(x+y)-x=0` , prove that `(dy)/(dx)=(1-x)/x`

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Given that,
`e^(x+y)-x=0`
`=>e^(x+y)=x`
`=>e^(x+y)[1+(dy)/(dx)]=1`
`=>(dy)/(dx)=(1-e^(x+y))/e^(x+y)`
`=>(dy)/(dx)=(1-x)/x`
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
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  2. If e^y=y^x , prove that (dy)/(dx)=((logy)^2)/(logy-1)

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  3. If e^(x+y)-x=0 , prove that (dy)/(dx)=(1-x)/x

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  11. If y=(sinx-cosx)^(sinx-cosx) ,pi/4 ltxlt (3pi)/ 4 find dy/dx

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  12. If x y=e^(x-y) , find (dy)/(dx) .

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  13. If y^x+x^y+x^x=a^b , find (dy)/(dx) .

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  14. If (cosx)^y=(cosy)^x find (dy)/(dx) .

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