derivative of arctan(x/(2000))

Lösung

\frac{d}{d x} (arctan (\frac{x}{2000}))

\frac{2000}{x ^{2} + 4000000}

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{x}{2000}))

Wende die Kettenregel an:

\frac{1}{( \frac{x}{2000} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{2000})

= \frac{1}{( \frac{x}{2000} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{2000})

\frac{d}{d x} (\frac{x}{2000}) = \frac{1}{2000}

= \frac{1}{( \frac{x}{2000} ) ^{2} + 1} \cdot \frac{1}{2000}

Vereinfache

\frac{1}{( \frac{x}{2000} ) ^{2} + 1} \cdot \frac{1}{2000} : \frac{2000}{x ^{2} + 4000000}

= \frac{2000}{x ^{2} + 4000000}

\int x \cdot \frac{e ^{x}}{2 x} d x

\frac{d}{d x} (x e^{3 z (x)})

t an g e n t f (x) = x^{3} + \frac{2}{x}, at x = 1

l a pl a ce t r an s f or m δ (t)

y^{^{'}} - 2 y = 5