derivative of arctan(x/b)

Lösung

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

\frac{b}{x ^{2} + b ^{2}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{b}{x ^{2} + b ^{2}}

\int sec^{2} (\frac{x}{2}) d x

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

s l o p e (1, - \frac{1}{2}), (- 2, - \frac{7}{2})

\frac{d}{d x} (\frac{tan ( 3 x ^{3} + x ^{2} )}{e ^{x}})^{3}

x \to 2 lim (- x^{2} + 2 x - 6)