derivative of cos((1-e^{6x}/(1+e^{6x)}))

Lösung

\frac{d}{d x} (cos (\frac{1 - e ^{6 x}}{1 + e ^{6 x}}))

\frac{12 e ^{6 x} sin ( \frac{1 - e ^{6 x}}{1 + e ^{6 x}} )}{( 1 + e ^{6 x} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (cos (\frac{1 - e ^{6 x}}{1 + e ^{6 x}}))

Wende die Kettenregel an:

- sin (\frac{1 - e ^{6 x}}{1 + e ^{6 x}}) \frac{d}{d x} (\frac{1 - e ^{6 x}}{1 + e ^{6 x}})

= - sin (\frac{1 - e ^{6 x}}{1 + e ^{6 x}}) \frac{d}{d x} (\frac{1 - e ^{6 x}}{1 + e ^{6 x}})

\frac{d}{d x} (\frac{1 - e ^{6 x}}{1 + e ^{6 x}}) = - \frac{12 e ^{6 x}}{( 1 + e ^{6 x} ) ^{2}}

= - sin (\frac{1 - e ^{6 x}}{1 + e ^{6 x}}) (- \frac{12 e ^{6 x}}{( 1 + e ^{6 x} ) ^{2}})

Vereinfache

- sin (\frac{1 - e ^{6 x}}{1 + e ^{6 x}}) (- \frac{12 e ^{6 x}}{( 1 + e ^{6 x} ) ^{2}}) : \frac{12 e ^{6 x} sin ( \frac{1 - e ^{6 x}}{1 + e ^{6 x}} )}{( 1 + e ^{6 x} ) ^{2}}

= \frac{12 e ^{6 x} sin ( \frac{1 - e ^{6 x}}{1 + e ^{6 x}} )}{( 1 + e ^{6 x} ) ^{2}}

x \to \infty lim (9.9)

y^{^{'}} = \frac{x - y}{x + y}

\frac{d}{d x} (e^{2 x} 0.2)

x \to 0 lim (x cot (x))

10 x - 8 y x^{2} + 1 y^{^{'}} = 0