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Beliebt Rechnen >

derivative of 3sin^5(x)

Lösung

\frac{d}{d x} (3 sin^{5} (x))

Lösung

15 sin^{4} (x) cos (x)

Schritte zur Lösung

\frac{d}{d x} (3 sin^{5} (x))

Entferne die Konstante:

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

= 3 \frac{d}{d x} (sin^{5} (x))

Wende die Kettenregel an:

5 (sin (x))^{4} \frac{d}{d x} (sin (x))

= 5 (sin (x))^{4} \frac{d}{d x} (sin (x))

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

= 3 \cdot 5 (sin (x))^{4} cos (x)

Vereinfache

= 15 sin^{4} (x) cos (x)

Graph

Beliebte Beispiele

derivative of (x+1(x+2))

\frac{d}{d x} ((x + 1) (x + 2))

(\partial)/(\partial x)(y^2-2ycos(x))

\frac{\partial}{\partial x} (y^{2} - 2 y cos (x))

\frac{d}{d t} (v (t))

derivative of ({f}(x)/({g)(x)})

\frac{d}{d x} (\frac{f ( x )}{g ( x )})

y^{''}+9y=2cos(3x)

y^{^{''}} + 9 y = 2 cos (3 x)