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Continuity And Differentiability

Question

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

Solution

Let space space space space space space space space space space straight y equals straight e to the power of negative straight x end exponent therefore space space space space space space dy over dx equals straight e to the power of negative straight x end exponent straight d over dx left parenthesis negative straight x right parenthesis equals straight e to the power of negative straight x end exponent left parenthesis negative 1 right parenthesis equals negative straight e to the power of negative straight x end exponent

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