What is the derivative of y=arccos(1/x) ?

The derivative of y=arccos(1/x) is (sqrt(x^2))/(x^2sqrt(x^2-1))

What is the first derivative of y=arccos(1/x) ?

The first derivative of y=arccos(1/x) is (sqrt(x^2))/(x^2sqrt(x^2-1))

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derivative

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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