derivative of arccot(sqrt(x^2))

Lösung

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

- \frac{x}{∣ x ∣ ( x ^{2} + 1 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{x}{∣ x ∣ ( x ^{2} + 1 )}

\frac{d}{d x} (3 e^{- 5 x})

d er i v a t i v e f (x) = x^{3} - 12 x^{2} + 45 x

\int \frac{x ^{2}}{2 x - 1} d x

\int x (4 - x) d x

t an g e n t f (x) = (\frac{x}{1 + x})^{5}, at x = 1