What is the derivative of arctan(x/8) ?

The derivative of arctan(x/8) is 8/(x^2+64)

What is the first derivative of arctan(x/8) ?

The first derivative of arctan(x/8) is 8/(x^2+64)

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\frac{d}{d x} (arctan (\frac{x}{8}))

\frac{8}{x ^{2} + 64}

Solution steps

\frac{d}{d x} (arctan (\frac{x}{8}))

Apply the chain rule:

\frac{1}{( \frac{x}{8} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{8})

= \frac{1}{( \frac{x}{8} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{8})

\frac{d}{d x} (\frac{x}{8}) = \frac{1}{8}

= \frac{1}{( \frac{x}{8} ) ^{2} + 1} \cdot \frac{1}{8}

Simplify

\frac{1}{( \frac{x}{8} ) ^{2} + 1} \cdot \frac{1}{8} : \frac{8}{x ^{2} + 64}

= \frac{8}{x ^{2} + 64}

\int x^{3} (\frac{1}{x} + 6 x^{2}) d x

\int 7 x^{6} sin (x^{7}) d x

\int x x^{2} - 3 d x

\frac{1}{s + 2}

8 x + 6, x - x^{2}, - 6, - 1

What is the derivative of arctan(x/8) ?
The derivative of arctan(x/8) is 8/(x^2+64)
What is the first derivative of arctan(x/8) ?
The first derivative of arctan(x/8) is 8/(x^2+64)