How to find the derivative of $3arccos(x/2)$ ?

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How to find the derivative of $3arccos(x/2)$ ?

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Answer 1 · 2015-04-16T02:33:03

- $3/[2sqrt(1-x^2/4)]$

Let y= 3 arc cos $x/2$ , so that $y/3$ = arc cos $x/2$
Thus, cos $y/3$ = $x/2$ and hence sin $y/3$ = $sqrt(1- x^2/4)$
Now differentiate, - $1/3$ sin $y/3$ $dy/dx$ = $1/2$

$dy/dx$ = - $3/[2sin(y/3)]$

= - $3/[2sqrt(1-x^2/4)]$

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How to find the derivative of $3arccos(x/2)$ ?

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