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351. Differentiate the following functions w.r.t.x:

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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352. Differentiate the following functions w.r.t.x:

tan left parenthesis straight x plus straight y right parenthesis plus tan left parenthesis straight x minus straight y right parenthesis equals 1

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353. Differentiate the following functions w.r.t.x:

log square root of straight x squared plus straight y squared end root equals tan to the power of negative 1 end exponent straight y over straight x

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Here space space space space space space space space straight x cubed plus straight y cubed equals sin left parenthesis straight x plus straight y right parenthesis 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 3 straight x squared plus 3 straight y squared dy over dx equals cos left parenthesis straight x plus straight y right parenthesis. open parentheses 1 plus dy over dx close parentheses therefore space 3 straight x squared plus 3 straight y squared dy over dx equals cos left parenthesis straight x plus straight y right parenthesis plus cos left parenthesis straight x plus straight y right parenthesis dy over dx therefore space left square bracket 3 straight y squared minus cos left parenthesis straight x plus straight y right parenthesis right square bracket dy over dx equals cos left parenthesis straight x plus straight y right parenthesis minus 3 straight x squared therefore space space space space dy over dx equals fraction numerator cos left parenthesis straight x plus straight y right parenthesis minus 3 straight x squared over denominator 3 straight y squared minus cos left parenthesis straight x plus straight y right parenthesis end fraction

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355.

Find space dy over dx when space straight x equals straight a left parenthesis straight theta plus sinθ right parenthesis comma space straight y equals straight a left parenthesis 1 minus cosθ right parenthesis

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356.

Find space dy over dx space when space straight x equals straight a left parenthesis 1 minus cosθ right parenthesis comma space straight y equals straight a left parenthesis straight theta plus sinθ right parenthesis

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357.

Find space dy over dx when space straight x equals straight a space sinθ comma space straight y equals straight a open parentheses cosθ plus log space tan straight theta over 2 close parentheses

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358.

Find space dy over dx space when space straight x equals cos cubed straight theta comma space straight y equals straight b space sin cubed straight theta

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359.

If space space straight x equals straight a left parenthesis 1 minus cosθ right parenthesis comma space straight y equals straight a left parenthesis 1 plus sinθ right parenthesis comma space find dy over dx comma

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360.

Find space dy over dx when space straight x equals straight a left parenthesis straight theta plus sinθ right parenthesis comma space straight y equals straight a left parenthesis 1 plus cosθ right parenthesis.

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