Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Continuity and Differentiability

Short Answer Type

351. Differentiate the following functions w.r.t.x: $sin left parenthesis straight x space straight y right parenthesis plus straight x over straight y equals straight x squared minus straight y$

Here space space sin left parenthesis straight x space straight y right parenthesis plus straight x over straight y equals straight x squared minus straight y Differentiating space both space sides space straight w. straight r. straight t. straight x comma cos left parenthesis straight x space straight y right parenthesis. straight d over dx left parenthesis straight x space straight y right parenthesis plus fraction numerator straight y space begin display style straight d over dx end style left parenthesis straight x right parenthesis minus straight x begin display style straight d over dx end style left parenthesis straight y right parenthesis over denominator straight y squared end fraction equals 2 straight x equals dy over dx therefore space cos left parenthesis straight x space straight y right parenthesis cross times open square brackets straight x dy over dx plus straight y.1 close square brackets plus fraction numerator straight y.1 minus straight x begin display style dy over dx end style over denominator straight y squared end fraction equals 2 straight x minus dy over dx therefore space straight x space straight y squared cos left parenthesis straight x space straight y right parenthesis dy over dx plus straight y cubed space cos left parenthesis straight x space straight y right parenthesis plus straight y minus straight x dy over dx equals 2 space straight x space straight y squared minus straight y squared dy over dx therefore space left square bracket straight x space straight y squared cos left parenthesis straight x space straight y right parenthesis minus straight x plus straight y squared right square bracket dy over dx equals 2 straight x space straight y squared minus straight y cubed space cos left parenthesis straight x space straight y right parenthesis minus straight y therefore space dy over dx equals fraction numerator straight y left square bracket 2 space straight x space straight y minus straight y squared cos left parenthesis straight x space straight y right parenthesis minus 1 right square bracket over denominator straight x space straight y squared cos left parenthesis straight x space straight y right parenthesis minus straight x plus straight y squared end fraction

74 Views

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

89 Views

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

91 Views

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

82 Views

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

83 Views

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

91 Views

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

91 Views

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

87 Views

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

82 Views

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.

84 Views