Derivata dell’arcoseno generalizzato

f(x)=\arcsin(\alpha\cdot x)

f'(x)=\frac{\alpha}{\sqrt{1-(\alpha\cdot x)^2}}

f(x)=\arcsin(3x)

f'(x)=\frac{3}{\sqrt{1-(3x)^2}}=\fbox{$\displaystyle\frac{3}{\sqrt{1-9x^2}}$}