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

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

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

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

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derivative of

arctan (\frac{x}{4})

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{4}) = \frac{1}{4}

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

Simplify

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

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

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