Continuity And Differentiability

Question

Differentiate the following w.r.t.x: $cot space straight x plus 2 cos space straight x plus 3 sin space straight x minus 1 half straight e to the power of straight x minus log space subscript straight a straight x$

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Solution

Let space space space space space straight y equals cot space straight x plus 2 cos space straight x plus 3 sin space straight x minus 1 half straight e to the power of straight x minus log subscript straight a straight x therefore space dy over dx equals negative cosec squared straight x minus 2 sin space straight x plus 3 cos space straight x minus 1 half straight e to the power of straight x minus 1 over straight x log subscript straight a straight x