What is the derivative of arccos(3/x) ?

The derivative of arccos(3/x) is 3/(xsqrt(x^2-9))

What is the first derivative of arccos(3/x) ?

The first derivative of arccos(3/x) is 3/(xsqrt(x^2-9))

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

\frac{3}{x x ^{2} - 9}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{1 - ( \frac{3}{x} ) ^{2}} (- \frac{3}{x ^{2}}) : \frac{3}{x x ^{2} - 9}

= \frac{3}{x x ^{2} - 9}

7 y^{^{''}} + 4 y^{^{'}} = 0

\int (t^{2} + 2)^{3} d t

\frac{d}{d t} (6 sin (t))

y = 4 x^{2}

x \to - 2 lim ((x^{2} - 1) (7 x + 3))

What is the derivative of arccos(3/x) ?
The derivative of arccos(3/x) is 3/(xsqrt(x^2-9))
What is the first derivative of arccos(3/x) ?
The first derivative of arccos(3/x) is 3/(xsqrt(x^2-9))