derivative of 5x^3cos(x)

Lösung

\frac{d}{d x} (5 x^{3} cos (x))

5 (3 x^{2} cos (x) - x^{3} sin (x))

Schritte zur Lösung

\frac{d}{d x} (5 x^{3} cos (x))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x^{3} cos (x))

Wende die Produktregel an:

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

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

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

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

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

= 5 (3 x^{2} cos (x) + (- sin (x)) x^{3})

Vereinfache

= 5 (3 x^{2} cos (x) - x^{3} sin (x))

\frac{\partial}{\partial x} (y x)

\frac{\partial}{\partial x} (3 y)

\int \frac{9}{x} d x

\frac{d}{d x} (x ln (2))

\frac{\partial}{\partial x} (x yz - tan (x + y + z))