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

2 square root of cot left parenthesis straight x squared right parenthesis end root

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Let space space space space space straight y equals 5 to the power of log space sin space straight x end exponent therefore space dy over dx equals 5 to the power of log space sin space straight x end exponent. log 5. straight d over dx left parenthesis log space sin space straight x right parenthesis equals 5 to the power of log space sin space straight x end exponent. log 5. fraction numerator 1 over denominator sin space straight x end fraction. straight d over dx left parenthesis sin space straight x right parenthesis space space space space space space space space space space space space space equals 5 to the power of log space sin space straight x end exponent. log 5. fraction numerator 1 over denominator sin space straight x end fraction. cos space straight x equals cot. log 5.5 to the power of log space sin space straight x end exponent

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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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