Question

How do you find the derivative of `g(x)=3 arccos (x/2)`?

Answer 1

`g'(x)=-3/(2sqrt(1-x^2/4)`

Explanation:

`•color(white)(x)cos^-1x=-1/sqrt(1-x^2)`

`"differentiate a composite function using the "`
`color(blue)"chain rule"`

`•color(white)(x)cos^-1(f(x))=-1/sqrt(1-(f(x))^2).f'(x)`

`g(x)=3cos^-1(x/2)`

`rArrg'(x)=3xx-1/sqrt(1-(x/2)^2)xx1/2`

`color(white)(rArrg'(x))=-3/(2sqrt(1-x^2/4))`