Limits and Derivatives

Limits and Derivatives

Question

Find the derivatives of the following functions :


(ax2+sin x) (p + q cos x)

Answer

Let y = (ax2+sin x) (p + q cos x)
Differentiating both sides w.r.t. x, we get

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space dy over dx equals straight d over dx left square bracket ax squared space plus sin space straight x right square bracket space straight d over dx left parenthesis straight p plus straight q space cos space straight x right parenthesis space plus space left parenthesis straight p space plus space straight q space cos space straight x right parenthesis space straight d over dx space left parenthesis ax squared plus sinx right parenthesis

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis ax squared plus sin space straight x right parenthesis space left square bracket 0 plus straight q left parenthesis negative sin space straight x right parenthesis right square bracket plus left parenthesis straight p plus straight q space cos space straight x 0 left square bracket 2 ax space plus cos space straight x right square bracket

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space minus straight q space sin space straight x left parenthesis ax squared plus sin space straight x right parenthesis space plus space left parenthesis space straight p plus straight w plus cos space straight x right parenthesis left parenthesis 2 ax space plus cos space straight x right parenthesis

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