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Continuity And Differentiability

Question

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Differentiate 7x⁵ - 11 x² w.r.t. 7x² - 15 x

Solution

Let space straight y equals 7 straight x to the power of 5 minus 11 space straight x squared space space and space straight u equals space 7 straight x squared minus 15 space straight x Then space it space is space required space to space find space dy over du Now space dy over du equals 35 straight x to the power of 4 minus 22 straight x space and space du over dx equals 14 straight x minus 15 therefore space space space space space dy over du equals fraction numerator dy over du over denominator du over dx end fraction equals fraction numerator 35 straight x to the power of 4 minus 22 straight x over denominator 14 straight x minus 15 end fraction.

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