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Lösung 1.2:2b

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The whole expression consists of two parts: the outer part, " e raised to something",


e 


where "something" is the inner part =x2+x. The derivative is calculated according to the chain rule by differentiating e  with respect to and then multiplying by the inner derivative  , i.e.


ddxex2+x=ex2+xx2+x 


The inner part is an ordinary polynomial which we differentiate directly:


ddxex2+x=ex2+x2x+1