derivative x^3cos(4x)

Lösung

ableitung von

x^{3} cos (4 x)

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{3}, g = cos (4 x)

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

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

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

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

Vereinfache

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

\int \frac{tan ^{3} ( x )}{sec ^{6} ( x )} d x

\int 1 - r^{2} r d r

x \to 4 lim (ln (x - 4))

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

\int_{0}^{3} 4 x - x^{2} d x