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Continuity And Differentiability

Question
CBSEENMA12034937

Differentiate the following functions w.r.t.x: straight x space cot cubed straight x

Solution
Let space straight y equals straight x space cot cubed straight x
space dy over dx equals straight x. straight d over dx left parenthesis cot cubed straight x right parenthesis plus cot cubed straight x. straight d over dx left parenthesis straight x right parenthesis equals straight x.3 cot squared straight x left parenthesis negative cosec squared straight x right parenthesis plus cot cubed straight x.1
space space space space space space space space space equals negative 3 straight x space cot squared straight x space cosec squared straight x plus cot cubed straight x

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