derivative of 6x^3cot(x)

Lösung

\frac{d}{d x} (6 x^{3} cot (x))

6 (3 x^{2} cot (x) - x^{3} csc^{2} (x))

Schritte zur Lösung

\frac{d}{d x} (6 x^{3} cot (x))

Entferne die Konstante:

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

= 6 \frac{d}{d x} (x^{3} cot (x))

Wende die Produktregel an:

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

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

= 6 (\frac{d}{d x} (x^{3}) cot (x) + \frac{d}{d x} (cot (x)) x^{3})

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

\frac{d}{d x} (cot (x)) = - csc^{2} (x)

= 6 (3 x^{2} cot (x) + (- csc^{2} (x)) x^{3})

Vereinfache

= 6 (3 x^{2} cot (x) - x^{3} csc^{2} (x))

s l o p e (2.4) (6.11)

\frac{\partial}{\partial y} (9 e^{x} cos (yz))

(f (x) e^{g (x)})^{'}

\frac{d}{d x} (x - x)

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