How do you find the derivative of #(arcsin(3x))/x#?
1 Answer
Jun 26, 2017
Explanation:
#"differentiate using the "color(blue)"quotient rule"#
#"given " f(x)=(g(x))/(h(x))" then"#
#f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larr" quotient rule"#
#color(orange)"Reminder"#
#• d/dx(sin^-1(f(x)))=1/(sqrt(1-(f(x))^2))xxf'(x)#
#g(x)=sin^-1(3x)rArrg'(x)=3/(sqrt(1-9x^2))#
#h(x)=xrArrh'(x)=1#
#rArrf'(x)=(x. 3/(sqrt(1-9x^2))-sin^-1(3x) .1)/x^2#
#color(white)(rArrf'(x))=((3x)/(sqrt(1-9x^2))-sin^-1(3x))/x^2#