What is the derivative of (arcsin(3x))/x?

1 Answer
Apr 23, 2015

You can solve this problem by using the quotient rule .

y=(arcsin(3x))/x=u/v

u=arcsin(3x)

sinu=3x

cosu*(du)/(dx)=3

(du)/(dx)=3/cosu=3/sqrt(1-9x^2)

v=x, (dv)/(dx)=1

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

(dy)/(dx)=1/(x^2)*{(3x)/sqrt(1-9x^2)-arcsin(3x)}