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

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Answer 1 · 2018-07-02T15:33:19

#f'(x)=\frac{3x-\sin^{-1}(3x)\sqrt{1-9x^2}}{x^2\sqrt{1-9x^2}}#

Given function

#f(x)=\frac{\sin^{-1}(3x)}{x}#

Using division rule, the derivative of given function

#f'(x)=\frac{d}{dx}(\frac{\sin^{-1}(3x)}{x})#

#=\frac{x\frac{d}{dx}(\sin^{-1}(3x))-\sin^{-1}(3x)\frac{d}{dx}x}{x^2}#

#=\frac{x\frac{1}{\sqrt{1-(3x)^2}}(3)-\sin^{-1}(3x)(1)}{x^2}#

#=\frac{\frac{3x}{\sqrt{1-9x^2}}-\sin^{-1}(3x)}{x^2}#

#=\frac{3x-\sin^{-1}(3x)\sqrt{1-9x^2}}{x^2\sqrt{1-9x^2}}#