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Question
Differentiate the following w.r.t. x : `cot^-1((sin3x)/(1 + cos3x))`
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Solution
Let y = `cot^-1((sin3x)/(1 + cos3x))`
= `cot^-1[(2sin((3x)/2)cos((3x)/2))/(2cos^2((3x)/2))]`
= `cot^-1[tan((3x)/2)]`
= `cot^-1[cot(pi/2 - (3x)/2)]`
= `pi/(2) - (3x)/(2)`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(pi/2 - (3x)/2)`
= `"d"/"dx"(pi/2) - (3)/(2)"dx"/"dx"`
= `0 - (3)/(2) xx 1`
= `-(3)/(2)`.
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