Question

Differentiate the following w.r.t.x:
cos (a cos x + b sin x), for some constants a and b.

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Solution

Let space space space space space straight y equals cos left parenthesis straight a space cos space straight x plus straight b space sin space straight x right parenthesis therefore space dy over dx equals negative sin left parenthesis straight a space cos space straight x plus straight b space sin space straight x right parenthesis. straight d over dx left parenthesis straight a space cos space straight x plus straight b space sin space straight x right parenthesis space space space space space space space space space space space space space equals negative sin left parenthesis straight a space cos space straight x plus straight b space sin space straight x right parenthesis. left parenthesis negative straight a space sin space straight x plus straight b space cos space straight x right parenthesis therefore space dy over dx equals left parenthesis straight a space sin space straight x minus straight b space cos space straight x right parenthesis. sin left parenthesis straight a space cos space straight x plus straight b space sin space straight x right parenthesis

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