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

1.	If sec (x+y) = xy, then find `(dy)/(dx)`
Answer» 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`

Discussion

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