How do you find the derivative of the function: $3arccos(x/2)$ ?

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Answer 1 · 2016-01-03T22:50:35

$3/sqrt(4-x^2)$

$d/dx(arccos(u))=-(u')/(sqrt(1-u^2))$

Thus,

$d/dx(3arccos(x/2))=3*(d/dx(x/2))/sqrt(1-(x/2)^2)$

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

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

How do you find the derivative of the function: 3arccos(x/2)3arccos(x/2)?