derivative of arctan(x^3-1)

Lösung

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

\frac{3 x ^{2}}{x ^{6} - 2 x ^{3} + 2}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{( x ^{3} - 1 ) ^{2} + 1} \cdot 3 x^{2} : \frac{3 x ^{2}}{x ^{6} - 2 x ^{3} + 2}

= \frac{3 x ^{2}}{x ^{6} - 2 x ^{3} + 2}

\frac{\partial}{\partial x} (- 2 y e^{x^{2} - y^{2}})

t a y l or e^{- 3 x + 1} + 8

\int \frac{e ^{2 t}}{e ^{2 t} - e ^{- 2 t}} d t

(sin (x^{2}))^{^{'}}

d er i v a t i v e x - sin (π x)