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

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}

Let space straight y equals straight x to the power of straight x plus left parenthesis 1 space plus space straight x right parenthesis to the power of log space straight x end exponent Put space straight x to the power of straight x equals straight u comma space left parenthesis 1 space plus space straight x right parenthesis to the power of log space straight x end exponent equals straight v therefore space straight y equals straight u plus straight v space 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 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 straight x to the power of straight x therefore space log space straight u equals log space straight x to the power of straight x therefore space 1 over straight u du over dx equals straight x.1 over straight x plus log space straight x.1 therefore space du over dx equals straight x to the power of straight x left square bracket 1 plus log space straight x right square bracket 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 space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis Also space straight v equals left parenthesis 1 space plus space straight x right parenthesis to the power of log space straight x end exponent therefore space log space straight v equals log left parenthesis 1 space plus space straight x right parenthesis to the power of log space straight x end exponent equals log left parenthesis 1 plus straight x right parenthesis therefore space 1 over straight v dv over dx equals left parenthesis log space straight x right parenthesis cross times fraction numerator 1 over denominator 1 plus straight x end fraction plus log left parenthesis 1 plus straight x right parenthesis therefore space dv over dx equals left parenthesis 1 space plus space straight x right parenthesis to the power of log space straight x end exponent open square brackets fraction numerator log space straight x over denominator 1 plus straight x end fraction plus fraction numerator log left parenthesis 1 plus straight x right parenthesis over denominator straight x 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... left parenthesis 3 right parenthesis From space left parenthesis 1 right parenthesis comma space left parenthesis 2 right parenthesis space and space left parenthesis 3 right parenthesis comma space we space get comma space space space space space dy over dx equals straight x to the power of straight x left parenthesis 1 plus log space straight x right parenthesis plus left parenthesis 1 plus straight x right parenthesis to the power of log space straight x end exponent open square brackets fraction numerator log space straight x over denominator 1 plus straight x end fraction plus fraction numerator log left parenthesis 1 plus straight x right parenthesis over denominator straight x end fraction close square brackets

73 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

Long Answer Type

Short Answer Type

270. Differentiate the following w.r.t. x xx + (1 + x)log x

270.
Differentiate the following w.r.t. x
x^x + (1 + x)^{log x}