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

straight x cubed plus straight y cubed equals sin left parenthesis straight x plus straight y right parenthesis

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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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space space space space space space space space space space space space space space space straight x equals straight a left parenthesis straight theta plus sinθ right parenthesis space rightwards double arrow space dx over xθ equals straight a left parenthesis 1 plus cosθ right parenthesis space space space space space space space space space space space space space space space straight y equals straight a left parenthesis 1 plus cosθ right parenthesis space rightwards double arrow space dx over dθ equals negative straight a space sinθ Now space dy over dx equals fraction numerator begin display style dy over dθ end style over denominator begin display style dx over dθ end style end fraction equals fraction numerator negative straight a space sinθ over denominator straight a left parenthesis 1 plus cosθ right parenthesis end fraction equals fraction numerator negative 2 sin begin display style straight theta over 2 end style cos begin display style straight theta over 2 end style over denominator cos begin display style straight theta over 2 end style end fraction equals negative fraction numerator sin begin display style straight theta over 2 end style over denominator cos begin display style straight theta over 2 end style end fraction equals negative tan straight theta over 2

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