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Continuity And Differentiability

Question

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Differentiate the following functions w.r.t.x: sin²x+cos²y=1

Solution

Here space space space space sin squared straight x plus cos squared straight y equals 1 Differentiating space both space sides space straight w. straight r. straight t. straight x comma space we space get comma space space space space space 2 sin space straight x space cos space straight x minus 2 cos space straight y space sin space straight y dy over dx equals 0 therefore space 2 cos space straight y space sin space straight y dy over dx equals 2 sin space straight x space cos space straight x therefore space space space space space space space space space space space sin space 2 straight y space dy over dx equals sin space 2 straight x therefore 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 sin space 2 straight x over denominator sin space 2 space straight y end fraction

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