How do you find the derivative of f(x) =(arcsin(3x))/x?

1 Answer
Mar 14, 2018

The answer would be (3*sqrt(1-9x^2))/(x*(1-9x^2))-arcsin(3x)/x^2

Explanation:

f(x)=arcsin(3x)/x

d/dx(arcsin(3x)/x)

=(d/dx(arcsin(3x))*x-d/dx(x)*arcsin(3x))/x^2

=((d/dx(3x))/sqrt(1-(3x)^2)-arcsin(3x))/x^2

=((3x)/sqrt(1-9x^2)-arcsin(3x))/x^2

=((3x)sqrt(1-9x^2))/((x^2)(1-9x^2))-arcsin(3x)/x^2

=(3sqrt(1-9x^2))/(x(1-9x^2))-arcsin(3x)/x^2