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Continuity And Differentiability

Question

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Differentiate the following functions w.r.t.x: $sin space straight y plus log space straight y equals straight x squared plus 18 straight x plus 3$

Solution

Here space sin space straight y plus log space straight y equals straight x squared plus 18 straight x plus 3 Differentiating space both space sides space straight w. straight r. straight t. straight x comma space we space get comma cos space straight y. dy over dx plus 1 over straight y dy over dx equals 2 straight x plus 18 therefore space open parentheses cos space straight y plus 1 over straight y close parentheses dy over dx equals 2 straight x plus 8 therefore space space space space space space space space space space fraction numerator straight y space cos space straight y plus 1 over denominator straight y end fraction equals 2 straight x plus 8 therefore 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 fraction numerator straight y left parenthesis 2 straight x plus 8 right parenthesis over denominator straight y space cos space straight y plus 1 end fraction

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