f(x)=arcsin(3x)/xf(x)=arcsin(3x)x
d/dx(arcsin(3x)/x)ddx(arcsin(3x)x)
=(d/dx(arcsin(3x))*x-d/dx(x)*arcsin(3x))/x^2=ddx(arcsin(3x))⋅x−ddx(x)⋅arcsin(3x)x2
=((d/dx(3x))/sqrt(1-(3x)^2)-arcsin(3x))/x^2=ddx(3x)√1−(3x)2−arcsin(3x)x2
=((3x)/sqrt(1-9x^2)-arcsin(3x))/x^2=3x√1−9x2−arcsin(3x)x2
=((3x)sqrt(1-9x^2))/((x^2)(1-9x^2))-arcsin(3x)/x^2=(3x)√1−9x2(x2)(1−9x2)−arcsin(3x)x2
=(3sqrt(1-9x^2))/(x(1-9x^2))-arcsin(3x)/x^2=3√1−9x2x(1−9x2)−arcsin(3x)x2