derivative of arctan(tanh(x))

Lösung

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

\frac{sech ^{2} ( x )}{tanh ^{2} ( x ) + 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (tanh (x)) = sech^{2} (x)

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

Vereinfache

\frac{1}{tanh ^{2} ( x ) + 1} sech^{2} (x) : \frac{sech ^{2} ( x )}{tanh ^{2} ( x ) + 1}

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

\int \frac{2 x ^{3} + 1}{x ^{2} + x - 6} d x

\int \frac{1}{2 x ^{2} - 4 x + 6} d x

\int_{0}^{1} 2 π x (33 - 33 x) d x

x \to 0 lim (\frac{\frac{4}{x + 4} - 1}{x})

\int_{0}^{1} \frac{73}{x ^{5}} d x