Differentiate the following functions w.r.t.x: from Mathematics

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 Multiple Choice QuestionsShort Answer Type

311. Differentiate the following functions w.r.t.x: log open parentheses square root of fraction numerator 1 minus cos space straight x over denominator 1 plus cos space straight x end fraction end root close parentheses
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312. Differentiate :log space sin square root of straight x squared plus 1 end root
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313.  If space straight y equals log square root of fraction numerator 1 plus cos squared straight x over denominator 1 minus straight e squared straight x end fraction end root comma space find space dy over dx
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314. If space equals log square root of fraction numerator 1 plus sin squared straight x over denominator 1 minus tan space straight x end fraction end root comma space find space dy over dx.
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315. Differentiate the following functions w.r.t.x:square root of 1 plus tan space straight x end root
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316. Differentiate the following functions w.r.t.x:square root of 1 plus cot space straight x end root
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317. Differentiate the following functions w.r.t.x:sin space 2 straight x. cos space 3 straight x


Here space space straight y equals sin space 2 straight x. cos space 3 straight x
therefore space dy over dx equals sin 2 straight x. straight d over dx left parenthesis cos space 3 straight x right parenthesis plus cos space 3 straight x. straight d over dx left parenthesis sin space 2 straight x right parenthesis
space space space space space space space space space space space space space equals sin space 2 straight x. left parenthesis negative 3 sin space 3 straight x right parenthesis plus cos space 3 straight x. left parenthesis 2 cos space 2 straight x right parenthesis
space space space space space space space space space space space space space equals negative 3 sin space 2 straight x space sin space 3 straight x plus 2 cos space 2 straight x space cos 3 straight x
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318. Differentiate the following functions w.r.t.x: straight x space cot cubed straight x
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319. Differentiate the following functions w.r.t.x:straight e to the power of negative straight x squared end exponent. sin left parenthesis log space straight x right parenthesis
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320. Differentiate the following functions w.r.t.x: straight e to the power of sin space straight x end exponent. sine to the power of straight x
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