What is the derivative of arccsc(tan(e^x)) ?

The derivative of arccsc(tan(e^x)) is -(e^xsec^2(e^x))/(tan(e^x)sqrt(tan^2(e^x)-1))

What is the first derivative of arccsc(tan(e^x)) ?

The first derivative of arccsc(tan(e^x)) is -(e^xsec^2(e^x))/(tan(e^x)sqrt(tan^2(e^x)-1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply the chain rule:

- \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}

Simplify

- \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}

What is the derivative of arccsc(tan(e^x)) ?
The derivative of arccsc(tan(e^x)) is -(e^xsec^2(e^x))/(tan(e^x)sqrt(tan^2(e^x)-1))
What is the first derivative of arccsc(tan(e^x)) ?
The first derivative of arccsc(tan(e^x)) is -(e^xsec^2(e^x))/(tan(e^x)sqrt(tan^2(e^x)-1))