What is the derivative of arccos((ax/2)) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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