What is (\partial)/(\partial x)(arctan(1/x)) ?

The answer to (\partial)/(\partial x)(arctan(1/x)) is -1/(1+x^2)

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(\partial)/(\partial x)(arctan(1/x))

\frac{\partial}{\partial x} (arctan (\frac{1}{x}))

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

Solution steps

\frac{\partial}{\partial x} (arctan (\frac{1}{x}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int e^{- s t} t sin (t) d t

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

x \to 1 + lim (\frac{∣ 1 - x ∣}{1 - x})

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

3 x^{2} - 16 x - 12

What is (\partial)/(\partial x)(arctan(1/x)) ?
The answer to (\partial)/(\partial x)(arctan(1/x)) is -1/(1+x^2)