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

Lösung

ableitung von

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}}

s l o p e (- 9, 3), (7, - 7)

\frac{d}{d x} (cos (e^{c o t (x^{2})}))

\frac{\partial}{\partial x} (x^{2} + 1)

\int - x^{2} sin (y) d y

\frac{d}{d x} ((arccot (x))^{5})