derivative of-6cot(xcsc(x))

Lösung

\frac{d}{d x} (- 6 cot (x) csc (x))

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

Schritte zur Lösung

\frac{d}{d x} (- 6 cot (x) csc (x))

Entferne die Konstante:

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

= - 6 \frac{d}{d x} (cot (x) csc (x))

Wende die Produktregel an:

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

f = cot (x), g = csc (x)

= - 6 (\frac{d}{d x} (cot (x)) csc (x) + \frac{d}{d x} (csc (x)) cot (x))

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} ((1 + 2 x^{2}) (x - x^{2}))

s l o p e in t erce pt (7.2) (2.8)

\int_{- 6}^{6} 58

x \to 4 lim (\frac{∣ x ∣}{x})

\frac{d}{d x} (\frac{1}{2 + x ^{2}})