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

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

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

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

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

- \frac{1}{1 + x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{1}{1 + x ^{2}}

\int_{4}^{\infty} x e^{- 2 x} d x

\int_{- 3}^{5} 2 y - (y^{2} - 15) d y

\frac{\partial}{\partial x} (3 x arctan (\frac{x}{y}))

4 e^{x} + x

\frac{d y}{d x} = - \frac{2 x}{y}

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