derivative g(t)=t^3cos(t)

Lösung

ableitung von

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

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

Schritte zur Lösung

\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)

= \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)

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

Vereinfache

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

\frac{d}{d x} (ln (2 x^{2} - 1))

x \to - 0.00000001 lim (x^{x})

d er i v a t i v e f (x) = [x + (x + sin^{2} (x))^{3}]^{4}

d er i v a t i v e f (x) = x^{2} + 5 - 3 x^{- 2}

x \to \infty lim ((\frac{13 x}{13 x + 3})^{5 x})