Question

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

Answer 1

`((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`