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

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

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

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

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derivative of

arctan (\frac{1 - x}{1 + x})

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

Solution steps

\frac{d}{d x} (arctan (\frac{1 - x}{1 + x}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to - \infty lim (81 x^{2} + x - 9 x)

n = 0 \sum \infty 9 (\frac{x}{7})^{n}

\frac{d}{d x} (x - 8 x)

y = 43 x^{2} + (x^{2})^{43}

x \to 2 lim (\frac{2 x ^{2}}{2 x + 2})

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