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Popular Calculus >

derivative of arccos((x+1/3))

Solution

\frac{d}{d x} (arccos (\frac{x + 1}{3}))

Solution

- \frac{1}{- x ^{2} - 2 x + 8}

Solution steps

\frac{d}{d x} (arccos (\frac{x + 1}{3}))

Apply the chain rule:

- \frac{1}{1 - ( \frac{x + 1}{3} ) ^{2}} \frac{d}{d x} (\frac{x + 1}{3})

= - \frac{1}{1 - ( \frac{x + 1}{3} ) ^{2}} \frac{d}{d x} (\frac{x + 1}{3})

\frac{d}{d x} (\frac{x + 1}{3}) = \frac{1}{3}

= - \frac{1}{1 - ( \frac{x + 1}{3} ) ^{2}} \cdot \frac{1}{3}

Simplify

- \frac{1}{1 - ( \frac{x + 1}{3} ) ^{2}} \cdot \frac{1}{3} : - \frac{1}{- x ^{2} - 2 x + 8}

= - \frac{1}{- x ^{2} - 2 x + 8}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of arccos((x+1/3)) ?
The derivative of arccos((x+1/3)) is -1/(sqrt(-x^2-2x+8))
What is the first derivative of arccos((x+1/3)) ?
The first derivative of arccos((x+1/3)) is -1/(sqrt(-x^2-2x+8))