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

1 Answer
Jim G.
Jun 26, 2017

#((3x)/sqrt(1-9x^2)-sin^-1(3x))/x^2#

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#

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