derivative of xln(x^2+4+4arctan(x/2)-2x)

Lösung

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

ln (x^{2} + 4)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d}{d x} (2 x) = 2

= ln (x^{2} + 4) + \frac{2 x ^{2}}{x ^{2} + 4} + \frac{8}{x ^{2} + 4} - 2

Vereinfache

ln (x^{2} + 4) + \frac{2 x ^{2}}{x ^{2} + 4} + \frac{8}{x ^{2} + 4} - 2 : ln (x^{2} + 4)

= ln (x^{2} + 4)

\frac{d}{d x} (cos (3 x))

\int x + 2 y d y

\int sin (x) cos (x) e^{s i n (x)} d x

n = 0 \sum \infty \frac{5 n}{n ^{2} + 4}

f (x) = \frac{e ^{x}}{ln ( x )}