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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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Here space 2 straight x plus 3 straight y equals sin space straight y Differentiating space both space sides space straight w. straight r. straight t. straight x comma space we space get comma straight d over dx left parenthesis 2 straight x right parenthesis plus straight d over dx left parenthesis 3 straight y right parenthesis equals straight d over dx left parenthesis sin space straight y right parenthesis therefore space 2 plus 3 dy over dx equals cos space straight y. dy over dx therefore space left parenthesis cos space straight y minus 3 right parenthesis dy over dx equals 2 therefore space dy over dx equals fraction numerator 2 over denominator cos space straight y minus 3 end fraction

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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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348.

Find space dy over dx space of space sin squared space straight y plus cos space straight x space straight y equals straight pi

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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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