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Question
tan–1(x2 + y2) = a
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Solution
Given that: tan–1(x2 + y2) = a
⇒ x2 + y2 = tan a.
Differentiating both sides w.r.t. x.
`"d"/"dx"(x^2 + y^2) = "d"/"dx"(tan "a")`
⇒ `2x + 2y * "dy"/"dx"` = 0
⇒ `2y * "dy"/"dx"` = – 2x
⇒ `"dy"/"dx" = (-2x)/(2y) = (-x)/y`
Hence, `"dy"/"dx" = (-x)/y`.
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