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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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Let space space space space space straight y equals straight e to the power of 3 straight x end exponent log left parenthesis sin space 2 straight x right parenthesis therefore space dy over dx equals straight e to the power of 3 straight x end exponent. straight d over dx left square bracket log left parenthesis sin space 2 straight x right parenthesis right square bracket plus log left parenthesis 2 sin space straight x right parenthesis. straight d over dx left parenthesis straight e to the power of 3 straight x end exponent right parenthesis space space space space space space space space space space space space space equals straight e to the power of 3 straight x end exponent. fraction numerator 1 over denominator sin space 2 straight x end fraction cross times 2 space cos space 2 straight x plus log left parenthesis sin space 2 straight x right parenthesis.3 straight e to the power of 3 straight x end exponent space space space space space space space space space space space space space equals straight e to the power of 3 straight x end exponent left square bracket 2 space cot space 2 straight x plus 3 log left parenthesis sin space 2 straight x right parenthesis right square bracket

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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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305.

Differentiate space straight e to the power of straight x space log square root of straight x. tan space straight x space straight w. straight r. straight t. straight x.

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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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