derivative of 1/2 arctan(x/2)

Lösung

\frac{d}{d x} (\frac{1}{2} arctan (\frac{x}{2}))

\frac{1}{x ^{2} + 4}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{2} arctan (\frac{x}{2}))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{d}{d x} (arctan (\frac{x}{2}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2} \cdot \frac{1}{( \frac{x}{2} ) ^{2} + 1} \cdot \frac{1}{2} : \frac{1}{x ^{2} + 4}

= \frac{1}{x ^{2} + 4}

d er i v a t i v e y = \frac{x ^{2} + 32 x}{8}

\int (x^{3} - 3 x) d x

\int_{2}^{5} e^{5 x} d x

x \to 1 lim (3 ln (x) + 4)

y^{^{''}} - 6 y^{^{'}} + 25 y = 0