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

261. Differentiate x.logx.log(log x)w.r.t.x.

84 Views

262.

If space straight x to the power of straight p. straight y to the power of straight q equals left parenthesis straight x plus straight y right parenthesis to the power of straight p plus straight q end exponent comma space show space that space dy over dx equals straight y over straight x

80 Views

Long Answer Type

263. Differentiate x^{log x} + (log x)^x w.r.t.x

73 Views

Short Answer Type

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

straight x to the power of straight x plus straight x to the power of log space straight x end exponent

73 Views

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

left parenthesis log space straight x right parenthesis to the power of straight x plus straight x to the power of log space straight x end exponent

73 Views

266. Differentiate the following functions w.r.t. x :
$open parentheses straight x plus 1 over straight x close parentheses to the power of straight x plus straight x to the power of open parentheses straight x plus 1 over straight x close parentheses end exponent$

Let space straight y equals open parentheses straight x plus 1 over straight x close parentheses to the power of straight x plus straight x to the power of open parentheses straight x plus 1 over straight x close parentheses end exponent Put space open parentheses straight x plus 1 over straight x close parentheses to the power of straight x equals straight u comma space straight x to the power of open parentheses straight x plus 1 over straight x close parentheses end exponent equals straight v therefore space straight y equals straight u plus straight v therefore space dy over dx equals du over dx plus dv over dx space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis Now space straight u equals open parentheses straight x plus 1 over straight x close parentheses to the power of straight x therefore space log space straight u equals log open parentheses straight x plus 1 over straight x close parentheses to the power of straight x therefore space log space straight u equals straight x. log open parentheses straight x plus 1 over straight x close parentheses therefore space 1 over straight u du over dx equals straight x. fraction numerator 1 over denominator straight x plus begin display style 1 over straight x end style end fraction. open parentheses straight x minus 1 over straight x squared close parentheses plus log open parentheses straight x plus 1 over straight x close parentheses.1 therefore space du over dx equals straight u open square brackets fraction numerator straight x squared over denominator straight x squared plus 1 end fraction cross times fraction numerator straight x squared minus 1 over denominator straight x squared end fraction plus log open parentheses straight x plus 1 over straight x close parentheses close square brackets therefore space du over dx equals open parentheses straight x plus 1 over straight x close parentheses to the power of straight x open square brackets fraction numerator straight x squared minus 1 over denominator straight x squared plus 1 end fraction plus log open parentheses straight x plus 1 over straight x close parentheses close square brackets Now space straight v equals straight x to the power of straight x plus 1 over straight x end exponent therefore space log space straight v equals log open parentheses bold x to the power of bold 1 bold plus bold 1 over bold x end exponent close parentheses therefore space log space straight v equals open parentheses 1 plus 1 over straight x close parentheses. log space straight x therefore space 1 over straight v dv over dx equals open parentheses 1 plus 1 over straight x close parentheses.1 over straight x plus left parenthesis log space straight x right parenthesis. open parentheses negative 1 over straight x squared close parentheses therefore space dv over dx equals straight v open square brackets fraction numerator straight x plus 1 over denominator straight x squared end fraction minus fraction numerator log space straight x over denominator straight x squared end fraction close square brackets therefore space dv over dx equals straight x to the power of straight x plus 1 over straight x end exponent open square brackets fraction numerator straight x plus 1 minus log space straight x over denominator straight x squared end fraction close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 3 right parenthesis From space left parenthesis straight i right parenthesis comma space left parenthesis 2 right parenthesis space and space left parenthesis 3 right parenthesis comma space we space get. space space space space space dy over dx equals open parentheses straight x plus 1 over straight x close parentheses to the power of straight x open square brackets fraction numerator straight x squared minus 1 over denominator straight x squared plus 1 end fraction plus log open parentheses straight x plus 1 over straight x close parentheses close square brackets plus straight x to the power of straight x plus 1 over straight x end exponent left parenthesis 1 plus straight x minus log space straight x right parenthesis

81 Views

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

straight x to the power of straight x to the power of 2 minus 3 end exponent end exponent plus left parenthesis straight x minus 3 right parenthesis to the power of straight x squared end exponent space for space straight x greater than 3

73 Views

268. Differentiate the following w.r.t. x :(log x)^{log x} + (1 + x)^2x

75 Views

269. Differentiate the following w.r.t. x :
x^x + x^1/x

76 Views

270.

Differentiate the following w.r.t. x
x^x + (1 + x)^{log x}

73 Views