Närmevärde till derivata – differenskvot

En del funktioner går inte att derivera med hjälp av de deriveringsregler som du lärt sig. Exempel på det är när man multiplicerar ihop delar som vardera lyder under olika regler. T.ex.: \[f(x)=x \cdot e^{2x} \]. Du vet hur du ska derivera x och potensen men inte hur du deriverar produkten mellan dem. Ifall det stått addition mellan x och potensen så hade du kunnat derivera dem var och en för sig men inte nu när det är en produkt dem emellan. Likaså om det är en division mellan två uttryck som du kan derivera nämnaren resp. täljaren men inte kvoten mellan dem. Ex: \[g(x)=\frac{x^2+1}{x+1} \]
Ingen av funktionerna ovan kan du derivera med de regler du hittills kan. Däremot kan du uppskatta derivatan av dem med hjälp av en metod som filmen behandlar.
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