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Beliebt Rechnen >

d/(dt)(4cos^3(t))

Lösung

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

Lösung

- 12 cos^{2} (t) sin (t)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

= 4 \cdot 3 (cos (t))^{2} (- sin (t))

Vereinfache

= - 12 cos^{2} (t) sin (t)

Graph

Beliebte Beispiele

derivative ((1))/((x^n+a^n))

d er i v a t i v e \frac{( 1 )}{( x ^{n} + a ^{n} )}

derivative 5x^2y^2

d er i v a t i v e 5 x^{2} y^{2}

derivative (-2y)/x

d er i v a t i v e \frac{- 2 y}{x}

derivative ((x^3-x))/((x^2))

d er i v a t i v e \frac{( x ^{3} - x )}{( x ^{2} )}

derivative ((-48x))/((x^2-16)^2)

d er i v a t i v e \frac{( - 48 x )}{( x ^{2} - 16 ) ^{2}}