What is the derivative of xarccos(1/x) ?

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

What is the first derivative of xarccos(1/x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (x arccos (\frac{1}{x}))

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

Solution steps

\frac{d}{d x} (x arccos (\frac{1}{x}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = arccos (\frac{1}{x})

= \frac{d x}{d x} arccos (\frac{1}{x}) + \frac{d}{d x} (arccos (\frac{1}{x})) x

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

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

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

Simplify

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

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

\int a e^{- b x} d x

\frac{d y}{d x} = y (1 - 0.0008 y)

\frac{d}{d x} (9 x + 7)

6 y^{^{''}} - 6 y^{^{'}} + 39 y = 0

x \to 0 lim ((1 + \frac{x}{2})^{\frac{3}{x}})

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