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Continuity And Differentiability

Question

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If sin x = y sin (x + b), show that $dy over dx equals fraction numerator sin space straight b over denominator sin squared left parenthesis straight x plus straight b right parenthesis end fraction$

Solution

because space space space sin space straight x equals space straight y space sin left parenthesis straight x plus straight b right parenthesis therefore space space space space space space space space space space straight y equals fraction numerator sin space straight x over denominator sin left parenthesis straight x plus straight b right parenthesis end fraction therefore space space space fraction numerator space dy over denominator dx end fraction equals fraction numerator sin left parenthesis straight x plus straight b right parenthesis space cos space straight x minus sin space straight x space cos space left parenthesis straight x plus straight b right parenthesis over denominator sin squared left parenthesis straight x plus straight b right parenthesis end fraction equals fraction numerator sin left square bracket left parenthesis straight x plus straight b right parenthesis minus straight x right square bracket over denominator sin squared left parenthesis straight x plus straight b right parenthesis end fraction equals fraction numerator sin space straight b over denominator sin squared left parenthesis straight x plus straight b right parenthesis end fraction

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