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Beliebt Rechnen >

derivative of cos^3(1-5x^2)

Lösung

\frac{d}{d x} (cos^{3} (1 - 5 x^{2}))

Lösung

30 x cos^{2} (1 - 5 x^{2}) sin (1 - 5 x^{2})

Schritte zur Lösung

\frac{d}{d x} (cos^{3} (1 - 5 x^{2}))

Wende die Kettenregel an:

3 (cos (1 - 5 x^{2}))^{2} \frac{d}{d x} (cos (1 - 5 x^{2}))

= 3 (cos (1 - 5 x^{2}))^{2} \frac{d}{d x} (cos (1 - 5 x^{2}))

\frac{d}{d x} (cos (1 - 5 x^{2})) = 10 x sin (1 - 5 x^{2})

= 3 (cos (1 - 5 x^{2}))^{2} \cdot 10 x sin (1 - 5 x^{2})

Vereinfache

= 30 x cos^{2} (1 - 5 x^{2}) sin (1 - 5 x^{2})

Graph

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