What is the derivative of arccos(sqrt(x)) ?

The derivative of arccos(sqrt(x)) is -1/(2sqrt(x)\sqrt{1-x)}

What is the first derivative of arccos(sqrt(x)) ?

The first derivative of arccos(sqrt(x)) is -1/(2sqrt(x)\sqrt{1-x)}

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derivative of

arccos (x)

- \frac{1}{2 x 1 - x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{1}{2 x 1 - x}

What is the derivative of arccos(sqrt(x)) ?
The derivative of arccos(sqrt(x)) is -1/(2sqrt(x)\sqrt{1-x)}
What is the first derivative of arccos(sqrt(x)) ?
The first derivative of arccos(sqrt(x)) is -1/(2sqrt(x)\sqrt{1-x)}