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

解答

\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}}

求解步骤

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

使用连锁律:

- 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}})

化简

- 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}}