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Popular >

derivative of arctan(((x-1)/((x+1))))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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