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Beliebt Rechnen >

derivative (arccot(x))^5

Lösung

ableitung von

(arccot (x))^{5}

Lösung

- \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

Schritte zur Lösung

\frac{d}{d x} ((arccot (x))^{5})

Wende die Kettenregel an:

5 (arccot (x))^{4} \frac{d}{d x} (arccot (x))

= 5 (arccot (x))^{4} \frac{d}{d x} (arccot (x))

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

= 5 (arccot (x))^{4} (- \frac{1}{x ^{2} + 1})

Vereinfache

5 arccot^{4} (x) (- \frac{1}{x ^{2} + 1}) : - \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

= - \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

Graph

Beliebte Beispiele

derivative of 3cos(x-5cot(x))

\frac{d}{d x} (3 cos (x) - 5 cot (x))

(xy^2)dx+(1+x^2y)dy=0

(x y^{2}) d x + (1 + x^{2} y) d y = 0

derivative of sqrt((4+8/x ^2+(2+x)^2))

\frac{d}{d x} (4 + \frac{8}{x})^{2} + (2 + x)^{2}

fläche y=sqrt(x^2-1),x=1,x=3

a re a y = x^{2} - 1, x = 1, x = 3

integral of 3xln(4x)

\int 3 x ln (4 x) d x