What is the derivative of y=arccos(9/x) ?

The derivative of y=arccos(9/x) is (9sqrt(x^2))/(x^2sqrt(x^2-81))

What is the first derivative of y=arccos(9/x) ?

The first derivative of y=arccos(9/x) is (9sqrt(x^2))/(x^2sqrt(x^2-81))

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derivative of

y = arccos (\frac{9}{x})

\frac{9 x ^{2}}{x ^{2} x ^{2} - 81}

Solution steps

\frac{d}{d x} (arccos (\frac{9}{x}))

Apply the chain rule:

- \frac{1}{1 - ( \frac{9}{x} ) ^{2}} \frac{d}{d x} (\frac{9}{x})

= - \frac{1}{1 - ( \frac{9}{x} ) ^{2}} \frac{d}{d x} (\frac{9}{x})

\frac{d}{d x} (\frac{9}{x}) = - \frac{9}{x ^{2}}

= - \frac{1}{1 - ( \frac{9}{x} ) ^{2}} (- \frac{9}{x ^{2}})

Simplify

- \frac{1}{1 - ( \frac{9}{x} ) ^{2}} (- \frac{9}{x ^{2}}) : \frac{9 x ^{2}}{x ^{2} x ^{2} - 81}

= \frac{9 x ^{2}}{x ^{2} x ^{2} - 81}

What is the derivative of y=arccos(9/x) ?
The derivative of y=arccos(9/x) is (9sqrt(x^2))/(x^2sqrt(x^2-81))
What is the first derivative of y=arccos(9/x) ?
The first derivative of y=arccos(9/x) is (9sqrt(x^2))/(x^2sqrt(x^2-81))