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

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Answer 1 · 2015-04-23T22:33:57

You can solve this problem by using the **quotient rule ** .

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

$u=arcsin(3x)$

$sinu=3x$

$cosu*(du)/(dx)=3$

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

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

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

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

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