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Continuity And Differentiability

Question

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$Find space dy over dx space when space straight x equals cos cubed straight theta comma space straight y equals straight b space sin cubed straight theta$

Solution

space space space space space space space space space space space straight x equals cos cubed straight theta therefore space dx over dθ equals 3 straight a space cos squared straight theta left parenthesis negative sinθ right parenthesis equals negative 3 acos squared θsinθ space space space space space space space space space space space straight y equals straight b space sin cubed straight theta therefore space dy over dθ equals 3 straight b space sin squared θcosθ Now space dy over dx equals fraction numerator begin display style dy over dθ end style over denominator begin display style dx over dθ end style end fraction equals fraction numerator 3 straight b space sin squared θcosθ over denominator negative 3 acos squared θsinθ end fraction

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