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Beliebt Rechnen >

derivative of sec(arctan(x))

Lösung

\frac{d}{d x} (sec (arctan (x)))

Lösung

\frac{x}{1 + x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (sec (arctan (x)))

Vereinfache

sec (arctan (x)) : 1 + x^{2}

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{2 1 + x ^{2}} \cdot 2 x

Vereinfache

\frac{1}{2 1 + x ^{2}} \cdot 2 x : \frac{x}{1 + x ^{2}}

= \frac{x}{1 + x ^{2}}

Graph

Beliebte Beispiele

derivative ln(ln(x/(2-x^2)))

d er i v a t i v e ln (ln (\frac{x}{2 - x ^{2}}))

limit as x approaches 5 of x^2-3x-10

x \to 5 lim (x^{2} - 3 x - 10)

\frac{d y}{d x} = 5 x y

(\partial)/(\partial x)(y^2-2xy-2x^2)

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

derivative f(x)=sqrt(5x+7)

d er i v a t i v e f (x) = 5 x + 7