Question

How do you differentiate `f(x) =arccos(2x + 1)`?

Answer 1

`f'(x)=-1/sqrt(-x^2-x).`

Explanation:

Recall that, `d/dt arc cos t=-1/sqrt(1-t^2).`

Therefore, `f(x)-arc cos(2x+1)`

`rArr f'(x)=-1/sqrt{1-(2x+1)^2}*d/dx(2x+1),...[because," The Chain Rule]."`

`rArr f'(x)=-2/sqrt(-4x^2-4x)=-1/sqrt(-x^2-x).`