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Question
If y = tan(x + y), find `("d"y)/("d"x)`
Solution
Given y = tan (x + y).
Differentiating both sides w.r.t. x, we have
`("d"y)/("d"x) = sec^2 (x + y) "d"/("d"x) (x + y)`
= `sec^2 (x + y) (1 + ("d"y)/("d"x))`
or `[1 - sec^2 (x + y)] ("d"y)/("d"x) = sec^2 (x + y)`
Therefore, `("d"y)/("d"x) = (sec^2(x + y))/(1 - sec^2(x + y)) = - "cosec"^2 (x + y)`
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