derivative of arccsc(tan(e^x))

解答

\frac{d}{d x} (arccsc (tan (e^{x})))

- \frac{e ^{x} sec ^{2} ( e ^{x} )}{tan ( e ^{x} ) tan ^{2} ( e ^{x} ) - 1}

求解步骤

\frac{d}{d x} (arccsc (tan (e^{x})))

使用连锁律:

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

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

\frac{d}{d x} (tan (e^{x})) = sec^{2} (e^{x}) e^{x}

= - \frac{1}{( tan ( e ^{x} ) ) ^{2} ( tan ( e ^{x} ) ) ^{2} - 1} sec^{2} (e^{x}) e^{x}

化简

- \frac{1}{tan ^{2} ( e ^{x} ) tan ^{2} ( e ^{x} ) - 1} sec^{2} (e^{x}) e^{x} : - \frac{e ^{x} sec ^{2} ( e ^{x} )}{tan ( e ^{x} ) tan ^{2} ( e ^{x} ) - 1}

= - \frac{e ^{x} sec ^{2} ( e ^{x} )}{tan ( e ^{x} ) tan ^{2} ( e ^{x} ) - 1}

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