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}

\frac{\partial}{\partial x} ((2 x + 3 x y^{2})^{2})

y = x^{2} + 3 x + 1, y = - x + 1

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

y = \frac{sin ( x ) + cos ( x )}{e ^{x}}

\frac{d}{d x} (- \frac{6 e ^{\frac{6}{x}}}{x ^{2}})

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)