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341. If cosy = x cos (a + y), then prove that

dy over dx equals fraction numerator cos squared left parenthesis straight a plus straight y right parenthesis over denominator sin space straight a end fraction

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342.

If space straight x space straight y plus straight y squared equals tan space straight x plus straight y comma space find dy over dx

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343.

Find space dy over dx space when space sin left parenthesis straight x space straight y right parenthesis plus straight x over straight y equals straight x squared minus straight y.

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344.

FInd space dy over dx of space 2 straight x plus 3 straight y equals sin space straight x.

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345.

FInd space dy over dx space of space 2 straight x plus 3 straight y equals sin space straight y

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346.

Find space dy over dx space of space straight a space straight x plus straight b space straight y squared equals cos space straight y space

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347.

Find space dy over dx space of space straight x space straight y plus straight y squared space equals tan space straight x plus straight y

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Here space space sin squared space straight y plus cos space straight x space straight y equals straight pi Differentiating space both space sides space straight w. straight r. straight t. straight x comma space we space get comma space straight d over dx left parenthesis sin squared straight y right parenthesis plus straight d over dx left parenthesis cos space straight x space straight y right parenthesis equals straight d over dx left parenthesis straight pi right parenthesis therefore space 2 sin space straight y dy over dx minus sin space straight x space straight y. straight d over dx left parenthesis straight x space straight y right parenthesis equals 0 therefore space 2 sin space straight y dy over dx minus sin space straight x space straight y. open parentheses straight x dy over dx plus straight y.1 close parentheses equals 0 therefore space 2 sin space straight y dy over dx minus straight x space sin space straight x space straight y. dy over dx minus straight y space sin space straight x space straight y equals 0 therefore space left parenthesis 2 space sin space straight v minus straight x space sin space xy right parenthesis dy over dx equals straight y space sin space straight x space straight y equals 0 therefore space dy over dx equals fraction numerator straight y space sin space xy over denominator 2 space sin space straight y minus straight x space sin space straight x space straight y end fraction

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

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350. 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

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