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Beliebt Rechnen >

d/(dt)(6sin^3(t))

Lösung

\frac{d}{d t} (6 sin^{3} (t))

Lösung

18 sin^{2} (t) cos (t)

Schritte zur Lösung

\frac{d}{d t} (6 sin^{3} (t))

Entferne die Konstante:

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

= 6 \frac{d}{d t} (sin^{3} (t))

Wende die Kettenregel an:

3 (sin (t))^{2} \frac{d}{d t} (sin (t))

= 3 (sin (t))^{2} \frac{d}{d t} (sin (t))

\frac{d}{d t} (sin (t)) = cos (t)

= 6 \cdot 3 (sin (t))^{2} cos (t)

Vereinfache

= 18 sin^{2} (t) cos (t)

Graph

Beliebte Beispiele

(d^2)/(dx^2)(5/(6t^4))

\frac{d ^{2}}{d x ^{2}} (\frac{5}{6 t ^{4}})

(dy)/(dx)=((x+y)^2)/(2x^2)

\frac{d y}{d x} = \frac{( x + y ) ^{2}}{2 x ^{2}}

derivative of x^2-4xy+y^2

\frac{d}{d x} (x^{2} - 4 x y + y^{2})

x^{2} y^{^{'}} + x y = 9

derivative of ln(x(x-1))

\frac{d}{d x} (ln (x) (x - 1))