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Continuity And Differentiability

Question

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$Differentiate space sin to the power of negative 1 end exponent straight theta space straight w. straight r. straight t. space log left parenthesis 1 plus straight theta right parenthesis$

Solution

Let space space space space space space space space space space straight y equals space sin to the power of negative 1 end exponent straight theta comma space straight u equals log left parenthesis 1 plus straight theta right parenthesis therefore space space space space space dy over dx equals fraction numerator 1 over denominator square root of 1 minus straight theta squared end root end fraction comma space du over dθ equals fraction numerator 1 over denominator 1 plus straight theta end fraction Now space dy over dx equals fraction numerator begin display style dy over dθ end style over denominator begin display style du over dθ end style end fraction equals fraction numerator 1 over denominator square root of 1 minus straight theta squared end root end fraction cross times fraction numerator 1 plus straight theta over denominator 1 end fraction equals fraction numerator 1 plus straight theta over denominator square root of 1 minus straight theta squared end root end fraction

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