What is the derivative of arctan(x/(sqrt(1-x^2))) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d x}{d t} + \frac{1}{t} x = t^{3} x^{4}

\frac{\partial}{\partial x} (\frac{4 x}{3 y})

\int \frac{6 x ^{2} + x + 25}{( x + 1 ) ( x ^{2} + 4 )} d x

(x^{3} - 9) x

\frac{2 w ^{3} - w}{w}

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