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291. Differentiate the following w.r.t.x:4cosxlog_ex+5

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292. Differentiate the following w.r.t.x:
cos (a cos x + b sin x), for some constants a and b.

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293. Differentiate (x² + 7 x + 2) (e^x - sin x) w.r.t.x.

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294. Differentiate sin³ x + cos⁶ x w.r.t.x.

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295. Differentiate cos x³. sin² (x⁵) w.r.t.x.

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Let space space space space space straight y equals fraction numerator straight e to the power of straight x over denominator sin space straight x end fraction therefore space dy over dx equals fraction numerator sin space straight x. begin display style straight d over dx end style left parenthesis straight e to the power of straight x right parenthesis minus straight e to the power of straight x. begin display style straight d over dx end style left parenthesis sin space straight x right parenthesis over denominator sin squared straight x end fraction space space space space space space space space space space space space space equals fraction numerator sin space straight x. straight e to the power of straight x minus straight e to the power of straight x space cos space straight x over denominator sin squared straight x end fraction equals straight e to the power of straight x open parentheses fraction numerator sin space straight x minus cos space straight x over denominator sin squared straight x end fraction close parentheses

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

fraction numerator cos space straight x over denominator log space straight x end fraction

, x>0

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

fraction numerator sin squared straight x over denominator 1 plus cos squared space straight x end fraction

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

fraction numerator straight e to the power of ax over denominator sin left parenthesis bx plus straight c right parenthesis end fraction

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

fraction numerator sin space straight x plus log space straight x over denominator straight x to the power of 7 plus straight e to the power of straight x end fraction

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