derivative f(x)=arccos(2x)

Lösung

ableitung von

f (x) = arccos (2 x)

- \frac{2}{1 - 4 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arccos (2 x))

Wende die Kettenregel an:

- \frac{1}{1 - ( 2 x ) ^{2}} \frac{d}{d x} (2 x)

= - \frac{1}{1 - ( 2 x ) ^{2}} \frac{d}{d x} (2 x)

\frac{d}{d x} (2 x) = 2

= - \frac{1}{1 - ( 2 x ) ^{2}} \cdot 2

Vereinfache

- \frac{1}{1 - ( 2 x ) ^{2}} \cdot 2 : - \frac{2}{1 - 4 x ^{2}}

= - \frac{2}{1 - 4 x ^{2}}

s l o p e in t erce pt (- 10, - 7), (- 5, - 9)

d o main f (x) = arctan (\frac{2 x}{1 - x ^{2}})

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