derivative of arccot(sqrt(2x))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

arccot (2 x) : arccot (2 x)

= \frac{d}{d x} (arccot (2 x))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (2 x) = \frac{1}{2 x}

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

Vereinfache

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

= - \frac{1}{2 x ( 2 x + 1 )}

x \to 1 + lim (\frac{x + 10}{x + 3})

d er i v a t i v e \frac{x ^{8} - 2 x ^{4} - 10 x}{x ^{4}}

a re a 6 ln (x), x ln (x)

\frac{d}{d t} (- 8 sin (t))

d er i v a t i v e - \frac{5}{x ^{4}}