derivative of-1/2 cot^3(x)

Lösung

\frac{d}{d x} (- \frac{1}{2} cot^{3} (x))

\frac{3}{2} cot^{2} (x) csc^{2} (x)

Schritte zur Lösung

\frac{d}{d x} (- \frac{1}{2} cot^{3} (x))

Entferne die Konstante:

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

= - \frac{1}{2} \frac{d}{d x} (cot^{3} (x))

Wende die Kettenregel an:

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

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

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

= - \frac{1}{2} \cdot 3 (cot (x))^{2} (- csc^{2} (x))

Vereinfache

- \frac{1}{2} \cdot 3 cot^{2} (x) (- csc^{2} (x)) : \frac{3}{2} cot^{2} (x) csc^{2} (x)

= \frac{3}{2} cot^{2} (x) csc^{2} (x)

\int - e^{y} d y

f (x) = ln (x) sin (x)

\frac{d}{d x} ((\frac{x - 6}{x + 7})^{3})

h \to + 0 lim (\frac{( 2 + h ) - 2}{h})

n = 0 \sum \infty \frac{n ^{2}}{n + 1}