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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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Let space space space space space straight y equals sin cubed straight x plus cos to the power of 6 straight x therefore space dy over dx equals 3 sin squared straight x straight d over dx left parenthesis sin space straight x right parenthesis plus 6 cos to the power of 5 straight x. straight d over dx left parenthesis cos space straight x right parenthesis space space space space space space space space space space space space space equals 3 sin squared straight x space cos space straight x plus 6 space cos to the power of 5 straight x. left parenthesis negative sin space straight x right parenthesis space space space space space space space space space space space space space equals 3 sin squared straight x space cos space straight x minus 6 sin space straight x space cos to the power of 5 straight x therefore space dy over dx equals 3 sin space straight x space cos space straight x left parenthesis sin space straight x minus 2 space cos to the power of 4 straight x right parenthesis

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

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

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

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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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