derivative of xcos(x^3)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (cos (x^{3})) = - sin (x^{3}) \cdot 3 x^{2}

= 1 \cdot cos (x^{3}) + (- sin (x^{3}) \cdot 3 x^{2}) x

Vereinfache

1 \cdot cos (x^{3}) + (- sin (x^{3}) \cdot 3 x^{2}) x : cos (x^{3}) - 3 x^{3} sin (x^{3})

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

\frac{d}{d x} (\frac{5 x ^{6}}{2} + \frac{12}{7 x ^{5}} - x)

\int \frac{4 x}{x - 8} d x

x \to 0 lim (arcsin (1 + 2 x))

\int_{1}^{5} \frac{7}{x ^{2}} d x

\frac{d}{d x} ((5 x + 8)^{3})