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Popular >

derivative of f(x)=arccos(e^x)

Solution

derivative of

f (x) = arccos (e^{x})

Solution

- \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}}

Popular Examples

(\partial)/(\partial y)(sqrt(x-y^2))

\frac{\partial}{\partial y} (x - y^{2})

limit as x approaches 0 of (6x^2)/(x^2)

x \to 0 lim (\frac{6 x ^{2}}{x ^{2}})

(\partial)/(\partial x)(e^{-x^5-y^3})

\frac{\partial}{\partial x} (e^{- x^{5} - y^{3}})

y+2y^'+5y=4*e^{-t}*cos(2t)

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\frac{x - 2}{x - 2}

Frequently Asked Questions (FAQ)

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