What is the derivative of 2arccos(x/4) ?

The derivative of 2arccos(x/4) is -2/(sqrt(16-x^2))

What is the first derivative of 2arccos(x/4) ?

The first derivative of 2arccos(x/4) is -2/(sqrt(16-x^2))

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\frac{d}{d x} (2 arccos (\frac{x}{4}))

- \frac{2}{16 - x ^{2}}

Solution steps

\frac{d}{d x} (2 arccos (\frac{x}{4}))

Take the constant out:

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

= 2 \frac{d}{d x} (arccos (\frac{x}{4}))

Apply the chain rule:

- \frac{1}{1 - ( \frac{x}{4} ) ^{2}} \frac{d}{d x} (\frac{x}{4})

= - \frac{1}{1 - ( \frac{x}{4} ) ^{2}} \frac{d}{d x} (\frac{x}{4})

\frac{d}{d x} (\frac{x}{4}) = \frac{1}{4}

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

Simplify

2 - \frac{1}{1 - ( \frac{x}{4} ) ^{2}} \cdot \frac{1}{4} : - \frac{2}{16 - x ^{2}}

= - \frac{2}{16 - x ^{2}}

f (x) = 2 sin (x), at x = \frac{π}{3}

\int x^{2} 6 x + 5 d x

f (x) = 3 a^{3 x}

9 x^{2} + y = 9, x^{4} - y = 1

\int \frac{3}{y} d y

What is the derivative of 2arccos(x/4) ?
The derivative of 2arccos(x/4) is -2/(sqrt(16-x^2))
What is the first derivative of 2arccos(x/4) ?
The first derivative of 2arccos(x/4) is -2/(sqrt(16-x^2))