What is the derivative of f(x)=3arccos(x/2) ?

The derivative of f(x)=3arccos(x/2) is -3/(sqrt(4-x^2))

What is the first derivative of f(x)=3arccos(x/2) ?

The first derivative of f(x)=3arccos(x/2) is -3/(sqrt(4-x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = 3 arccos (\frac{x}{2})

- \frac{3}{4 - x ^{2}}

Solution steps

\frac{d}{d x} (3 arccos (\frac{x}{2}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (arccos (\frac{x}{2}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

= 3 - \frac{1}{1 - ( \frac{x}{2} ) ^{2}} \cdot \frac{1}{2}

Simplify

3 - \frac{1}{1 - ( \frac{x}{2} ) ^{2}} \cdot \frac{1}{2} : - \frac{3}{4 - x ^{2}}

= - \frac{3}{4 - x ^{2}}

\frac{d}{d x} (\frac{3 x}{5 x ^{2} - 2 x - 9})

y = x^{2} - 18, y = 17 x

\int_{e}^{e^{8}} \frac{1}{x ln ( x ^{7} )} d x

\frac{d y}{d x} = e^{- x} + y

\frac{d y}{d x} = 3 x^{2} - 7

What is the derivative of f(x)=3arccos(x/2) ?
The derivative of f(x)=3arccos(x/2) is -3/(sqrt(4-x^2))
What is the first derivative of f(x)=3arccos(x/2) ?
The first derivative of f(x)=3arccos(x/2) is -3/(sqrt(4-x^2))