derivative of xarctan(x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = arctan (x)

= \frac{d x}{d x} arctan (x) + \frac{d}{d x} (arctan (x)) x

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

2 y^{^{''}} - y^{^{'}} + 3 y = 0

x^{2} y^{^{''}} - 14 x y^{^{'}} + 56 y = 0

\int (\frac{x ^{3} + 2 x ^{2} - 4}{x ^{2}}) d x

\int_{1}^{2} x - 1 d x

in v erse l a pl a ce \frac{3 s}{( s ^{2} + 4 )}