What is the derivative of arccot(e^x) ?

The derivative of arccot(e^x) is -(e^x)/(e^{2x)+1}

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

The first derivative of arccot(e^x) is -(e^x)/(e^{2x)+1}

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

- \frac{e ^{x}}{e ^{2 x} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (e^{x}) = e^{x}

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

Simplify

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

= - \frac{e ^{x}}{e ^{2 x} + 1}

What is the derivative of arccot(e^x) ?
The derivative of arccot(e^x) is -(e^x)/(e^{2x)+1}
What is the first derivative of arccot(e^x) ?
The first derivative of arccot(e^x) is -(e^x)/(e^{2x)+1}