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Beliebt Rechnen >

(a(t)sin^3(t))^'

Lösung

(a (t) sin^{3} (t))^{^{'}}

Lösung

a (sin^{3} (t) + 3 t sin^{2} (t) cos (t))

Schritte zur Lösung

(a (t) sin^{3} (t))^{'}

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= a (t sin^{3} (t))^{^{'}}

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = sin^{3} (t)

= a (t^{^{'}} sin^{3} (t) + (sin^{3} (t))^{^{'}} t)

t^{'} = 1

(sin^{3} (t))^{'} = 3 sin^{2} (t) cos (t)

= a (1 \cdot sin^{3} (t) + 3 sin^{2} (t) cos (t) t)

Vereinfache

= a (sin^{3} (t) + 3 t sin^{2} (t) cos (t))

Graph

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