Föreläsning 3

Lärare: Anna Delin

Innehåll: Introduktion till derivata, Adams 2.1-2.5.

Nyckelbegrepp

Tangentlinje

Tangentlinjens lutning

Vertikal och icke-vertikal tangentlinje

En kurvas lutning i en punkt

https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/calculus--derivatives-1--new-hd-version

Normalen

https://www.khanacademy.org/math/differential-calculus/derivative_applications/normal-tangent-line-eq/v/normal-line-equation

Derivata, formell definition

https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/alternate-form-of-the-derivative

Deriverbar funktion, ej deriverbar funktion, kontinuitet

https://www.khanacademy.org/math/differential-calculus/taking-derivatives/visualizing-derivatives-tutorial/v/where-a-function-is-not-differentiable

Deriveringssymboler

Deriveringsregler för polynom, trigonometriska funktioner, rötter

https://www.khanacademy.org/math/differential-calculus/taking-derivatives/power_rule_tutorial/v/power-rule

Derivata av en produkt av två funktioner

https://www.khanacademy.org/math/differential-calculus/taking-derivatives/product_rule/v/applying-the-product-rule-for-derivatives

Derivata av en kvot av två funktioner

https://www.khanacademy.org/math/differential-calculus/taking-derivatives/product_rule/v/quotient-rule-from-product-rule

Derivata av en sammansatt funktion - inre derivata - kedjeregeln

https://www.khanacademy.org/math/differential-calculus/taking-derivatives/chain_rule/v/chain-rule-introduction