What is the derivative of arcsin(x/(1+x^2)) ?

The derivative of arcsin(x/(1+x^2)) is (1-x^2)/((x^2+1)sqrt(x^4+x^2+1))

What is the first derivative of arcsin(x/(1+x^2)) ?

The first derivative of arcsin(x/(1+x^2)) is (1-x^2)/((x^2+1)sqrt(x^4+x^2+1))

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

\frac{1 - x ^{2}}{( x ^{2} + 1 ) x ^{4} + x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{1 - ( \frac{x}{1 + x ^{2}} ) ^{2}} \cdot \frac{1 - x ^{2}}{( 1 + x ^{2} ) ^{2}} : \frac{1 - x ^{2}}{( x ^{2} + 1 ) x ^{4} + x ^{2} + 1}

= \frac{1 - x ^{2}}{( x ^{2} + 1 ) x ^{4} + x ^{2} + 1}

\frac{d}{d x} (\frac{( 2 π - x cos ( x ) )}{x - 2 π})

\frac{( 3 x ^{2} - 4 ) ( x ^{2} - 6 )}{x ^{2} + 4}

\frac{\partial}{\partial y} (\frac{x}{y + x})

\frac{d}{d x} ((x^{2} + 3)^{s i n (x)})

e^{3 t} (9 - 4 t + 10 sin (\frac{t}{2}))

What is the derivative of arcsin(x/(1+x^2)) ?
The derivative of arcsin(x/(1+x^2)) is (1-x^2)/((x^2+1)sqrt(x^4+x^2+1))
What is the first derivative of arcsin(x/(1+x^2)) ?
The first derivative of arcsin(x/(1+x^2)) is (1-x^2)/((x^2+1)sqrt(x^4+x^2+1))