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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 x^{sin x}w.r.t. (sin x)^x

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Let space space space space space straight y equals sin space straight x squared comma space straight u equals straight x squared therefore space dy over dx equals left parenthesis cos space straight x squared right parenthesis comma space 2 straight x equals 2 straight x space cos space straight x squared space space space space space du over dx equals 2 straight x Now space dy over du equals fraction numerator begin display style dy over dx end style over denominator begin display style du over dx end style end fraction equals fraction numerator 2 straight x space cos space straight x squared over denominator 2 straight x end fraction equals cos space straight x squared

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379. Differentiate cos(x^x) w.r.t.x.

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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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