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(dy)/(dx)-(tanx)/(1+x)e^(x) secy...

`(dy)/(dx)-(tanx)/(1+x)e^(x) secy`

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(dy)/(dx)-(tanx)/(1+x)=(1+x)e^(x) secy

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(x-y)(1-(dy)/(dx))=e^(x)

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

Find (dy)/(dx) where y=(tanx)/(x)

e^(-x) (dy)/(dx) = y(1+ tanx + tan^(2) x)