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Continuity And Differentiability

Question

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Differentiate the following w.r.t.x: $straight e to the power of sin to the power of negative 1 end exponent straight x end exponent$

Solution

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

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