Question

Find the derivative of f(x)=2arcsin(x-1)

Answer 1

Since $\dfrac{\mathrm d}{\mathrm dx}\arcsin x=\dfrac1{\sqrt{1-x^2}$, you have

$\displaystyle\frac{\mathrm d}{\mathrm dx}2\arcsin(x-1)=2\frac{\mathrm d}{\mathrm dx}\arcsin(x-1)=2\frac{\dfrac{\mathrm d}{\mathrm dx}(x-1)}{\sqrt{1-(x-1)^2}=\frac2{\sqrt{2x-x^2}}$