derivative of arctan((3x/2))

Lösung

\frac{d}{d x} (arctan (\frac{3 x}{2}))

\frac{6}{9 x ^{2} + 4}

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{3 x}{2}))

Wende die Kettenregel an:

\frac{1}{( \frac{3 x}{2} ) ^{2} + 1} \frac{d}{d x} (\frac{3 x}{2})

= \frac{1}{( \frac{3 x}{2} ) ^{2} + 1} \frac{d}{d x} (\frac{3 x}{2})

\frac{d}{d x} (\frac{3 x}{2}) = \frac{3}{2}

= \frac{1}{( \frac{3 x}{2} ) ^{2} + 1} \cdot \frac{3}{2}

Vereinfache

\frac{1}{( \frac{3 x}{2} ) ^{2} + 1} \cdot \frac{3}{2} : \frac{6}{9 x ^{2} + 4}

= \frac{6}{9 x ^{2} + 4}

\int (tan (x))^{- 1} d x

\frac{\partial}{\partial x} (lo g_{10} (x))

x^{^{'}} = x - 4

\frac{d}{d x} (cos (x) + \frac{1}{x})

\frac{\partial}{\partial x} (2 cos (π x))