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Beliebt Rechnen >

derivative 4t^3cos(t)

Lösung

ableitung von

4 t^{3} cos (t)

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

integral from-infinity to 12 of re^{r/3}

\int_{- \infty}^{12} r e^{\frac{r}{3}} d r

(\partial)/(\partial t)(xyz^2tan(yt))

\frac{\partial}{\partial t} (x y z^{2} tan (y t))

tangent x^2+xy-y^2=-9,(3,6)

t an g e n t x^{2} + x y - y^{2} = - 9, (3, 6)

maclaurin (2x)/(1+x^2)

ma c l a u r in \frac{2 x}{1 + x ^{2}}

fläche F(x)=ln(2x),y=0,y=2

a re a F (x) = ln (2 x), y = 0, y = 2