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

The derivative of arccos(e^x) is -(e^x)/(sqrt(1-e^{2x))}

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to - 1 lim (- x^{2})

ln (2 t)

\int \frac{1}{x ^{2} x ^{2} + 36} d x

x \to 2 lim (x^{3} + x^{2} - 5 x + 1)

\int \frac{x + 1}{x ^{5}} d x

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