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#