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

The derivative of (arcsin(3x))/x is (3x-arcsin(3x)sqrt(1-9x^2))/(x^2sqrt(1-9x^2))

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

The first derivative of (arcsin(3x))/x is (3x-arcsin(3x)sqrt(1-9x^2))/(x^2sqrt(1-9x^2))

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derivative of

\frac{arcsin ( 3 x )}{x}

\frac{3 x - arcsin ( 3 x ) 1 - 9 x ^{2}}{x ^{2} 1 - 9 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{arcsin ( 3 x )}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( arcsin ( 3 x ) ) x - \frac{d x}{d x} arcsin ( 3 x )}{x ^{2}}

\frac{d}{d x} (arcsin (3 x)) = \frac{3}{1 - 9 x ^{2}}

\frac{d x}{d x} = 1

= \frac{\frac{3}{1 - 9 x ^{2}} x - 1 \cdot arcsin ( 3 x )}{x ^{2}}

Simplify

\frac{\frac{3}{1 - 9 x ^{2}} x - 1 \cdot arcsin ( 3 x )}{x ^{2}} : \frac{3 x - arcsin ( 3 x ) 1 - 9 x ^{2}}{x ^{2} 1 - 9 x ^{2}}

= \frac{3 x - arcsin ( 3 x ) 1 - 9 x ^{2}}{x ^{2} 1 - 9 x ^{2}}

x \to 1 lim (2 x + 2)

\frac{d ^{2}}{d x ^{2}} (x^{\frac{3}{2}})

\int \frac{- 1}{x ^{2} + 16} d x

\frac{d}{d x} (\frac{x ^{2} - 3 x}{2 x + 1})

\frac{s}{9 s + 81}

What is the derivative of (arcsin(3x))/x ?
The derivative of (arcsin(3x))/x is (3x-arcsin(3x)sqrt(1-9x^2))/(x^2sqrt(1-9x^2))
What is the first derivative of (arcsin(3x))/x ?
The first derivative of (arcsin(3x))/x is (3x-arcsin(3x)sqrt(1-9x^2))/(x^2sqrt(1-9x^2))