What is the derivative of arctan(4/x) ?

The derivative of arctan(4/x) is -4/(16+x^2)

What is the first derivative of arctan(4/x) ?

The first derivative of arctan(4/x) is -4/(16+x^2)

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derivative of

arctan (\frac{4}{x})

- \frac{4}{16 + x ^{2}}

Solution steps

\frac{d}{d x} (arctan (\frac{4}{x}))

Apply the chain rule:

\frac{1}{( \frac{4}{x} ) ^{2} + 1} \frac{d}{d x} (\frac{4}{x})

= \frac{1}{( \frac{4}{x} ) ^{2} + 1} \frac{d}{d x} (\frac{4}{x})

\frac{d}{d x} (\frac{4}{x}) = - \frac{4}{x ^{2}}

= \frac{1}{( \frac{4}{x} ) ^{2} + 1} (- \frac{4}{x ^{2}})

Simplify

\frac{1}{( \frac{4}{x} ) ^{2} + 1} (- \frac{4}{x ^{2}}) : - \frac{4}{16 + x ^{2}}

= - \frac{4}{16 + x ^{2}}

\frac{d y}{d x} + y = \frac{e ^{x}}{y}

\int_{3}^{4} e^{3 - x} d x

\int \frac{1}{6 x ^{6}} d x

ln (x), \frac{4}{x}, 1, 3

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

What is the derivative of arctan(4/x) ?
The derivative of arctan(4/x) is -4/(16+x^2)
What is the first derivative of arctan(4/x) ?
The first derivative of arctan(4/x) is -4/(16+x^2)