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If tan (x+y) = xy, then find (dy)/(dx)...

If tan (x+y) = xy, then find `(dy)/(dx)`

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We have, sec (x+y)=xy
On differentiating both sides w.r.t x, we get
`sec (x+y)cdot tan (x+y) cdot (d)/(dx) (x+y) = x (dy)/(dx)+y`
`rArr overset(cdot)sec (x+y) cdot tan (x+y) cdot (1+(dy)/(dx))=x(dy)/(dx)+y`
`rArr (dy)/(dx)[sec (x+y)cdot tan (x+y)-x]`
`=y-sec (x+y)cdot. tan (x+y)`
`therefore (dy)/(dx)=(y-sec(x+y).tan (x+y))/(sec (x+y). tan (x+y)-x`
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