derivative y=cos^4(x)

Lösung

ableitung von

y = cos^{4} (x)

- 4 cos^{3} (x) sin (x)

Schritte zur Lösung

\frac{d}{d x} (cos^{4} (x))

Wende die Kettenregel an:

4 (cos (x))^{3} \frac{d}{d x} (cos (x))

= 4 (cos (x))^{3} \frac{d}{d x} (cos (x))

\frac{d}{d x} (cos (x)) = - sin (x)

= 4 (cos (x))^{3} (- sin (x))

Vereinfache

= - 4 cos^{3} (x) sin (x)

h \to 0 lim (3 x^{2} + 2 x h + h^{2})

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\frac{\partial}{\partial x} (arccos (\frac{y}{x}))

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