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281. Differentiate w.r.t.x:

space straight y equals sin left parenthesis ax plus straight b right parenthesis

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282. Differentiate w.r.t.x:

cos left parenthesis square root of straight x right parenthesis

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

cos left parenthesis sin space straight x right parenthesis

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

sec left parenthesis tan left parenthesis square root of straight x right parenthesis right parenthesis

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Let space space space space space straight y equals 2 square root of cot left parenthesis straight x squared right parenthesis end root equals 2 left square bracket cot left parenthesis straight x squared right parenthesis right square bracket to the power of 1 half end exponent therefore space dy over dx equals 2.1 half left square bracket cot left parenthesis straight x squared right parenthesis right square bracket to the power of negative 1 half end exponent. straight d over dx left parenthesis cot space straight x squared right parenthesis space space space space space space space space space space space space space equals fraction numerator 1 over denominator square root of cot space straight x squared end root end fraction. left parenthesis negative cosec squared straight x squared right parenthesis. straight d over dx left parenthesis cot space straight x squared right parenthesis space space space space space space space space space space space space space equals fraction numerator 1 over denominator square root of cot space straight x squared end root end fraction. left parenthesis negative cosec squared straight x squared right parenthesis. left parenthesis 2 straight x right parenthesis equals negative fraction numerator 2 straight x space cosec squared straight x squared over denominator square root of cot space straight x squared end root end fraction

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286. Differentiate 5^{log sin x} w.r.t.x.

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

straight e to the power of straight x plus 3 sec space straight x plus log space straight x squared

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

cot space straight x plus 2 cos space straight x plus 3 sin space straight x minus 1 half straight e to the power of straight x minus log space subscript straight a straight x

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289.

Find space dy over dx comma space when space straight y equals 3 tan space straight x plus 5 space log subscript straight a straight x plus square root of straight x minus 3 straight e to the power of straight x plus 1 over straight x.

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290. Differentiate the following w.r.t.x: e^x sin x

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