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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (x^{2} y + 4 y)

\int \frac{- 5 x}{( x ^{2} + 5 ) ^{\frac{3}{2}}} d x

y = x ln (sin^{2} (x))

y (x + 7) + \frac{d y}{d x} = 0

\int \frac{- 1}{\frac{1}{4} - x ^{2}} d x

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