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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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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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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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