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Continuity And Differentiability

Question

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Differentiate the following w.r.t.x: $straight e to the power of sin square root of straight x end exponent$

Solution

Let space space space space straight y equals straight e to the power of sin square root of straight x end exponent therefore space dy over dx equals straight e to the power of sin square root of straight x end exponent. straight d over dx left parenthesis sin square root of straight x right parenthesis equals straight e to the power of sin square root of straight x end exponent. cos square root of straight x cross times fraction numerator 1 over denominator 2 square root of straight x end fraction equals fraction numerator straight e to the power of sin square root of straight x end exponent. cos square root of straight x over denominator 2 square root of straight x end fraction

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