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

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

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

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

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\frac{d}{d 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}}

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