What is the derivative of arccos((12/x)) ?

The derivative of arccos((12/x)) is (12)/(xsqrt(x^2-144))

What is the first derivative of arccos((12/x)) ?

The first derivative of arccos((12/x)) is (12)/(xsqrt(x^2-144))

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\frac{d}{d x} (arccos (\frac{12}{x}))

\frac{12}{x x ^{2} - 144}

Solution steps

\frac{d}{d x} (arccos (\frac{12}{x}))

Apply the chain rule:

- \frac{1}{1 - ( \frac{12}{x} ) ^{2}} \frac{d}{d x} (\frac{12}{x})

= - \frac{1}{1 - ( \frac{12}{x} ) ^{2}} \frac{d}{d x} (\frac{12}{x})

\frac{d}{d x} (\frac{12}{x}) = - \frac{12}{x ^{2}}

= - \frac{1}{1 - ( \frac{12}{x} ) ^{2}} (- \frac{12}{x ^{2}})

Simplify

- \frac{1}{1 - ( \frac{12}{x} ) ^{2}} (- \frac{12}{x ^{2}}) : \frac{12}{x x ^{2} - 144}

= \frac{12}{x x ^{2} - 144}

\int \frac{sin ( x )}{1 + 2 cos ( x )} d x

\frac{d y}{d x} y = x^{- 8}

\int \frac{1}{( 1 - 6 t ) ^{4}} d t

cos^{2} (3 t)

What is the derivative of arccos((12/x)) ?
The derivative of arccos((12/x)) is (12)/(xsqrt(x^2-144))
What is the first derivative of arccos((12/x)) ?
The first derivative of arccos((12/x)) is (12)/(xsqrt(x^2-144))