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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (arctan (\frac{1}{x}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

7 t

\frac{d}{d x} (cot (π x))

x \to 2 + lim (\frac{x}{x - 3})

\frac{d}{d x} (lo g_{3} (x) \cdot (x^{3} + 2))

n \to \infty lim (2^{n + 1})

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