derivative of arctanh(sqrt(3x))

Lösung

\frac{d}{d x} (arctanh (3 x))

\frac{3}{2 x ( 1 - 3 x )}

Schritte zur Lösung

\frac{d}{d x} (arctanh (3 x))

Vereinfache

arctanh (3 x) : arctanh (3 x)

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{1 - ( 3 x ) ^{2}} \cdot \frac{3}{2 x} : \frac{3}{2 x ( 1 - 3 x )}

= \frac{3}{2 x ( 1 - 3 x )}

d er i v a t i v e ln (\frac{x ^{2}}{2 x ^{2} + 3 x + 2})

\int x - 25 - x^{2} d x

\frac{\partial}{\partial x} (2 x^{4} + 3 y^{3} + 2 x y)

\int \frac{4 x ^{2} + 2 x - 1}{x ^{3} + x ^{2}} d x

\frac{d}{d x} (a - x)