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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 lim (\frac{e ^{x} - 1}{16 x})

\frac{d}{d x} (x^{4} - 8 x^{2} + 1)

\int arcsin (y) d y

\int_{- \infty}^{0} \frac{1}{1 + x ^{2}} d x

\frac{d}{d x} (ln (5 x + 1))

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