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Beliebt Rechnen >

derivative of sqrt(x^2-4)-2arcsec(x/2)

Lösung

\frac{d}{d x} (x^{2} - 4 - 2 arcsec (\frac{x}{2}))

Lösung

\frac{x ^{2} - 4}{x}

Schritte zur Lösung

\frac{d}{d x} (x^{2} - 4 - 2 arcsec (\frac{x}{2}))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{2} - 4) - \frac{d}{d x} (2 arcsec (\frac{x}{2}))

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

\frac{d}{d x} (2 arcsec (\frac{x}{2})) = \frac{4}{x x ^{2} - 4}

= \frac{x}{x ^{2} - 4} - \frac{4}{x x ^{2} - 4}

Vereinfache

\frac{x}{x ^{2} - 4} - \frac{4}{x x ^{2} - 4} : \frac{x ^{2} - 4}{x}

= \frac{x ^{2} - 4}{x}

Graph

Beliebte Beispiele

limit as x approaches infinity of e^{5xln(1+1/x)}

x \to \infty lim (e^{5 x l n (1 + \frac{1}{x})})

integral of (4x^3-5sqrt(x))/x

\int \frac{4 x ^{3} - 5 x}{x} d x

(\partial)/(\partial x)(r/x)

\frac{\partial}{\partial x} (\frac{r}{x})

integral of 1/(x^2sqrt(64x^2+81))

\int \frac{1}{x ^{2} 64 x ^{2} + 81} d x

(dy)/(dx)=((x-1))/(y-4)

\frac{d y}{d x} = \frac{( x - 1 )}{y - 4}