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301. Differentiate the following w.r.t.x:

fraction numerator straight e to the power of straight x over denominator 1 plus cos space straight x end fraction

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302. Differentiate the following w.r.t.x:

straight e to the power of sin square root of straight x end exponent

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303. Differentiate the following w.r.t.x:

straight e to the power of 3 straight x end exponent log left parenthesis sin space 2 straight x right parenthesis

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304. Differentiate the following w.r.t.x:

straight e to the power of square root of 1 minus straight x squared end root end exponent

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Let space space space space space straight y equals straight e to the power of straight x space log space straight x to the power of 1 half end exponent tan space straight x space equals 1 half straight e to the power of straight x log space straight x. tan space straight x therefore space dy over dx equals 1 half open square brackets straight e to the power of straight x log space straight x. straight d over dx left parenthesis tan space straight x right parenthesis plus straight e to the power of straight x tan space straight x straight d over dx left parenthesis log space straight x right parenthesis plus log space straight x. tanx straight d over dx left parenthesis straight e to the power of straight x right parenthesis close square brackets space space space space space space space space space space space space space equals 1 half open square brackets straight e to the power of straight x log space xsec squared straight x plus fraction numerator straight e to the power of straight x tanx over denominator straight x end fraction plus log space xtan space straight x. straight e to the power of straight x close square brackets space space space space space space space space space space space space space equals 1 half straight e to the power of straight x open square brackets log space straight x. sec squared straight x plus fraction numerator tan space straight x over denominator straight x end fraction plus log space straight x. tan space straight x close square brackets

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

sin left parenthesis log space straight x right parenthesis

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

straight e to the power of cos space straight x end exponent

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

log left parenthesis cos space 5 straight x right parenthesis

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

log space sin left parenthesis straight e to the power of straight x plus 5 straight x plus 8 right parenthesis

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

log space tan open parentheses straight pi over 4 plus straight x over 2 close parentheses

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