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Popular >

derivative of arccos(x/pi)

Solution

\frac{d}{d x} (arccos (\frac{x}{π}))

Solution

- \frac{1}{π ^{2} - x ^{2}}

Solution steps

\frac{d}{d x} (arccos (\frac{x}{π}))

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{1}{π ^{2} - x ^{2}}

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\int_{0}^{1} x cos (x) d x

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\int_{2}^{6} x^{2} d x

Frequently Asked Questions (FAQ)

What is the derivative of arccos(x/pi) ?
The derivative of arccos(x/pi) is -1/(sqrt(pi^2-x^2))
What is the first derivative of arccos(x/pi) ?
The first derivative of arccos(x/pi) is -1/(sqrt(pi^2-x^2))