Differentiate cos(xx) w.r.t.x. from Mathematics Continuity and
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    Continuity and Differentiability

    Multiple Choice QuestionsShort Answer Type

    371. Differentiate space cos space straight x times cos space 2 straight x. cos 3 straight x space space straight w. straight r. straight t. straight x.
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    372. Find space dy over dx comma space if space straight y equals left parenthesis sin space straight x right parenthesis to the power of sin space straight x to the power of sin space straight x... infinity end exponent end exponent
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    373. If space straight y equals left parenthesis cos right parenthesis to the power of cos space straight x to the power of cos space straight x..... infinity end exponent end exponent comma space prove space that space dy over dx equals negative fraction numerator straight y squared tan space straight x over denominator 1 minus straight y space log space cos space straight x end fraction
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    374. If space straight y equals left parenthesis tan space straight x right parenthesis to the power of tan space straight x to the power of tan space straight x.... infinity end exponent end exponent comma space prove space that space dy over dx equals 2 space at space straight x equals straight pi over 2
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    375. Differentiate (log x)cos x w.r.t. x.
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    376. Differentiate (log x)sin x w.r.t.x.
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    377. Differentiate xsin xw.r.t. (sin x)x
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    378.  Differentiate sin x2w.r.t.x2.
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    379. Differentiate cos(xx) w.r.t.x.

    Let space space space space space space space straight y equals cos left parenthesis straight x to the power of straight x right parenthesis therefore space space space space space space space space space straight y equals cos space straight u space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis where space straight u equals straight x to the power of straight x therefore space log space straight u equals log space straight x to the power of straight x space rightwards double arrow space log space straight u equals straight x space log space straight x therefore space 1 over straight u du over dx equals straight x.1 over straight x plus log space straight x.1 space rightwards double arrow space du over dx equals straight x to the power of straight x left parenthesis 1 plus log space straight x right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis From space left parenthesis 1 right parenthesis comma space dy over dx equals negative sin space straight u du over dx therefore space dy over dx equals negative sin left parenthesis straight x to the power of straight x right parenthesis. straight x to the power of straight x left parenthesis 1 plus log space straight x right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket because space of space left parenthesis 2 right parenthesis right square bracket therefore space dy over dx equals negative straight x to the power of straight x left parenthesis 1 plus log space straight x right parenthesis. sin left parenthesis straight x to the power of straight x right parenthesis
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    380. Differentiate space straight x to the power of tan space straight x end exponent plus square root of fraction numerator straight x squared plus 1 over denominator straight x end fraction end root straight w. straight r. straight t. straight x.
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