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sec(x+y)= xy |
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Answer» On differentiatingboth sidesw.r.t. we get ` (d)/(DX) sec (x+y) = d/(dx) (xy)` `RARR sec (x+y).tan(x+y).(d)/(dx)(x+y)=x.d/dx y+y.(d)/(dx) x` `rArr sec(x+y). tan(x+y).(1+(DY)/(dx)) = x '(dy)(dx) +y` `rArr sec(x+y)tan(x+y)+sec(x+y).tan(x+y).(dy)/(dx)=x'(dy)/(dx) + y` `rArr (dy)/(dx) [sec (x+y).tan(x+y)-x] = y - sec(x+y).tan(x+y)` `:. (dy)/(dx) = (y-sec(x+y).tan(x+y))/(sec(x+y).tan(x+y)-x)` |
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