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

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Answer 1 · 2018-03-14T18:41:04

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

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

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

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

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

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

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

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

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