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

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

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

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

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

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

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