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Beliebt Rechnen >

derivative cos(2arctan(x/2))

Lösung

ableitung von

cos (2 arctan (\frac{x}{2}))

Lösung

- \frac{4 sin ( 2 arctan ( \frac{x}{2} ) )}{x ^{2} + 4}

Schritte zur Lösung

\frac{d}{d x} (cos (2 arctan (\frac{x}{2})))

Wende die Kettenregel an:

- sin (2 arctan (\frac{x}{2})) \frac{d}{d x} (2 arctan (\frac{x}{2}))

= - sin (2 arctan (\frac{x}{2})) \frac{d}{d x} (2 arctan (\frac{x}{2}))

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

= - sin (2 arctan (\frac{x}{2})) \frac{4}{x ^{2} + 4}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{4 sin ( 2 arctan ( \frac{x}{2} ) )}{x ^{2} + 4}

Graph

Beliebte Beispiele

integral of (u^2)/(sqrt(u^2-8u))

\int \frac{u ^{2}}{u ^{2} - 8 u} d u

derivative of x^{1/3}(x+4)

\frac{d}{d x} (x^{\frac{1}{3}} (x + 4))

derivative 2/(1+3x+x^2)

d er i v a t i v e \frac{2}{1 + 3 x + x ^{2}}

(24+x^2)y^'-2xy=0

(24 + x^{2}) y^{^{'}} - 2 x y = 0

(dy}{dx}=\frac{y^3)/x ,y(1)=1

\frac{d y}{d x} = \frac{y ^{3}}{x}, y (1) = 1