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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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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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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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