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

1 Answer
Jim G.
Jun 26, 2017

((3x)/sqrt(1-9x^2)-sin^-1(3x))/x^23x√1−9x2−sin−1(3x)x2

Explanation:

"differentiate using the "color(blue)"quotient rule"differentiate using the quotient rule

"given " f(x)=(g(x))/(h(x))" then"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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