What is the derivative of (arccos(x)/x) ?

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

What is the first derivative of (arccos(x)/x) ?

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

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

\frac{- x - arccos ( x ) 1 - x ^{2}}{x ^{2} 1 - x ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

Simplify

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

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

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

\int 4 - x d x

x \to - \infty lim (x^{2} + 2)

\int_{1}^{2} 3 x^{2} d x

\int \frac{1}{x ^{2} + 4 x + 3} d x

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