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Question
Differentiate the following w.r.t. x : `tan^-1((a + btanx)/(b - atanx))`
Solution
Let y = `tan^-1((a + btanx)/(b - atanx))`
= `tan^-1[(a/b + tanx)/(1 - a/b.tanx)]`
= `tan^-1(a/b) + tan^-1(tanx)`
= `tan^-1(a/b) + x`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[tan^-1(a/b) + x]`
= `"d"/"dx"[tan^-1(a/b)] + "d"/"dx"(x)`
= 0 + 1
= 1.
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